Skip to main content
Fachgebiete
Automobil + Motoren Bauwesen + Immobilien Business IT + Informatik Elektrotechnik + Elektronik Energie + Nachhaltigkeit Finance + Banking Management + Führung Marketing + Vertrieb Maschinenbau + Werkstoffe Versicherung + Risiko
DE
EN
Bücher
Zeitschriften
Themenseiten
Organisationspsychologie Projektmanagement Marketing Smart Manufacturing
Weitere Formate
Podcasts Webinare Technik Webinare Wirtschaft Kongresse Veranstaltungskalender Awards
Jetzt Einzelzugang starten
Zugang für Unternehmen
Referenzkunden
SLX-Digitalkonferenz: Zukunftswerkstatt 2024

Mehr Umsatz mit Top-Kontakten

Am 7. Mai erfahren Sie, wie Vertriebsteams Leadgenerierung, Leadnurturing und Leadstrategien effizient steuern können.
Erweiterte Suche
Anmelden
nach oben
Erschienen in:
Measurement Principles and Structures Kapitel lesen Erstes Kapitel lesen

2006 | OriginalPaper | Buchkapitel

22. Monte Carlo Simulation

verfasst von : Xiao Hu, Associate Professor, Yoshihiko Nonomura, Ph.D., Masanori Kohno, Dr.

Erschienen in: Springer Handbook of Materials Measurement Methods

Verlag: Springer Berlin Heidelberg

Einloggen

Aktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.

search-config
loading …

Abstract

In the general overview on materials and their characteristics, outlined in chapter 3, it has been stated that materials and their characteristics result from the processing of matter. Thus, condensed matter physics is one of the fundamentals for the understanding of materials. The Monte Carlo Method, which is a powerful method in this respect, is presented in this final chapter of the Handbook's Part E on Modelling and Simulation Methods as follows:
First, the principles of this simulation technique are introduced
  • Monte Carlo Method: the fundamentals
  • Improved Monte Carlo algorithms
  • Quantum Monte Carlo Method
Second, the application of the Monte Carlo Method is explained in considering selected areas of materials science:
  • Electronic correlations: antiferromagnetism
  • Perfect conductance of electricity: superconductivity
  • Vortex states in condensed matter physics
  • Quantum critical phenomena

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Jetzt informieren

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

Jetzt informieren

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 340 Zeitschriften

aus folgenden Fachgebieten:

  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Versicherung + Risiko




Jetzt Wissensvorsprung sichern!

Jetzt informieren
Vorheriges Kapitel Phase Field
Literatur
22.1.
K. Binder, Q. W. Heermann: Monte Carlo Simulation in Statistical Physics, Springer Series in Solid-State Sciences (Springer-Verlag, Germany 1988) p. 80
22.2.
N. Metropolis, A. W. Rosenbluth, M. N. Rosenbluth, A. H. Teller, E. Teller: Equation of State Calculations by Fast Computing Machines, J. Chem. Phys. 21, 1087–1092 (1953)
22.3.
A. M. Ferrenberg, D. P. Landau, Y. J. Wong: Monte Carlo simulations: Hidden errors from “good” random number generators, Phys. Rev. Lett. 69, 3382–3384 (1992)
22.4.
M. Matsumoto, Y. Kurita: Twisted GFSR generators, ACM Trans. Model. Comput. Siml. 2, 179–194 (1992)
22.5.
M. Matsumoto, Y. Kurita: Twisted GFSR generators II, ACM Trans. Model. Comput. Siml. 4, 254–266 (1994)
22.6.
M. Matsumoto, T. Nishimura: Mersenne Twister: A 623-dimensionally equidistributed uniform pseudorandom number generator, ACM Trans. Model. Comput. Siml. 8, 3–30 (1998)
22.7.
22.8.
M. Suzuki: Linear and nonlinear dynamic scaling relations in the renormalization group theory, Phys. Lett. A 58, 435–436 (1976)
22.9.
M. Suzuki: Static and dynamic finite-size scaling theory based on the renormalization group approach, Prog. Theor. Phys. 83, 1142–1150 (1977)
22.10.
N. Ito: Non-equilibrium critical relaxation of the three-dimensional Ising model, Physica A 192, 604–616 (1993)
22.11.
N. Ito, T. Matsuhisa, H. Kitatani: Ferromagnetic transition of ± J Ising spin glass model on square lattice, J. Phys. Soc. Jpn. 67, 1188–1196 (1998)
22.12.
N. Ito, K. Hukushima, K. Ogawa, Y. Ozeki: Nonequilibrium relaxation of fluctuations of physical quantities, J. Phys. Soc. Jpn. 69, 1931–1934 (2000)
22.13.
Z. B. Li, L. Schülke, B. Zheng: Dynamic Monte Carlo measurement of critical exponents, Phys. Rev. Lett. 74, 3396–3398 (1995)
22.14.
Y. Nonomura: New quantum Monte Carlo approach to ground-state phase transitions in quantum spin systems, J. Phys. Soc. Jpn. 67, 5–7 (1998)
22.15.
Y. Nonomura: New quantum Monte Carlo study of quantum critical phenomena with Trotter-number-dependent finite-size scaling and non-equilibrium relaxation, J. Phys. A 31, 7939–7954 (1998)
22.16.
T. Nakamura, Y. Ito: A quantum Monte Carlo algorithm realizing an intrinsic relaxation, J. Phys. Soc. Jpn. 72, 2405–2408 (2003)
22.17.
Y. Ozeki, K. Ogawa, N. Ito: Nonequilibrium relaxation analysis of Kosterlitz-Thouless phase transition, Phys. Rev. E 67, 026007(1–5) (2003)
22.18.
Y. Ozeki, K. Kasono, N. Ito, S. Miyashita: Nonequilibrium relaxation analysis for first-order phase transitions, Physica A 321, 271–279 (2003)
22.19.
Y. Iba: Extended ensemble Monte Carlo, Int. J. Mod. Phys. C 12, 623–656 (2001)
22.20.
A. M. Ferrenberg, R. H. Swendsen: New Monte Carlo technique for studying phase transitions, Phys. Rev. Lett. 61, 2635–2638 (1988)
22.21.
A. M. Ferrenberg, R. H. Swendsen: Optimized Monte Carlo data analysis, Phys. Rev. Lett. 63, 1195–1198 (1989)
22.22.
A. M. Ferrenberg, D. P. Landau: Critical behavior of the three-dimensional Ising model: A high-resolution Monte Carlo study, Phys. Rev. B 44, 5081–5091 (1991)
22.23.
B. A. Berg, T. Neuhaus: Multicanonical algorithms for first order phase transitions, Phys. Lett. B 267, 249–253 (1991)
22.24.
B. A. Berg, T. Neuhaus: Multicanonical ensemble: A new approach to simulate first-order phase transitions, Phys. Rev. Lett. 68, 9–12 (1992)
22.25.
J. Lee: New Monte Carlo algorithm: Entropic sampling, Phys. Rev. Lett. 71, 211–214 (1993)
22.26.
P. M. C. de Oliveira, T. J. P. Penna, H. J. Herrmann: Broad histogram method, Braz. J. Phys. 26, 677–683 (1996)
22.27.
P. M. C. de Oliveira, T. J. P. Penna, H. J. Herrmann: Broad histogram Monte Carlo, Eur. Phys. J. B 1, 205–208 (1998)
22.28.
R. H. Swendsen, B. Diggs, J.-S. Wang, S.-T. Li, C. Genovese, J. B. Kadane: Transition matrix Monte Carlo, Int. J. Mod. Phys. C 10, 1563–1569 (1999)
22.29.
J.-S. Wang, T. K. Tay, R. H. Swendsen: Transition matrix Monte Carlo reweighting and dynamics, Phys. Rev. Lett. 82, 476–479 (1999)
22.30.
J.-S. Wang: Flat histogram Monte Carlo method, Physica A 281, 147–150 (2000)
22.31.
F. Wang, D. P. Landau: Efficient, multiple-range random walk algorithm to calculate the density of states, Phys. Rev. Lett. 86, 2050–2053 (2001)
22.32.
F. Wang, D. P. Landau: Determining the density of states for classical statistical models: A random walk algorithm to produce a flat histogram, Phys. Rev. E 64, 1–16 (2001)
22.33.
J. Lee, J. M. Kosterlitz: New numerical method to study phase transitions, Phys. Rev. Lett. 65, 137–140 (1990)
22.34.
J. Lee, J. M. Kosterlitz: Finite-size scaling and Monte Carlo simulations of first-order phase transitions, Phys. Rev. B 43, 3265–3277 (1991)
22.35.
R. H. Swendsen, J.-S. Wang: Nonuniversal critical dynamics in Monte Carlo simulations, Phys. Rev. Lett. 58, 86–88 (1987)
22.36.
P. W. Kasteleyn, C. M. Fortuin: Phase transitions in lattice systems with random local properties, J. Phys. Soc. Jpn. Suppl. 26, 11–14 (1969)
22.37.
C. M. Fortuin, P. W. Kasteleyn: On the random cluster model. I: Introduction and relation to other models, Physica 57, 536–564 (1972)
22.38.
U. Wolff: Collective Monte Carlo updating for spin systems, Phys. Rev. Lett. 62, 361–364 (1989)
22.39.
P. Tamayo, R. C. Brower, W. Klein: Single-cluster Monte-Carlo dynamics for the Ising-model, J. Stat. Phys. 58, 1083–1094 (1990)
22.40.
H. G. Evertz, G. Lana, M. Marcu: Cluster algorithm for vertex models, Phys. Rev. Lett. 70, 875–879 (1993)
22.41.
J. Machta, Y. S. Choi, A. Lucke, T. Schweizer, L. V. Chayes: Invaded cluster algorithm for equilibrium critical points, Phys. Rev. Lett. 75, 2792–2795 (1995)
22.42.
J. Machta, Y. S. Choi, A. Lucke, T. Schweizer, L. V. Chayes: Invaded cluster algorithm for Potts models, Phys. Rev. E 54, 1332–1345 (1996)
22.43.
Y. Tomita, Y. Okabe: Probability-changing cluster algorithm for Potts models, Phys. Rev. Lett. 86, 572–575 (2001)
22.44.
N. Prokof'ev, B. Svistunov: Worm algorithms for classical statistical models, Phys. Rev. Lett. 87, 160601(1–4) (2001)
22.45.
F. Matsubara, T. Iyota, S. Inawashiro: Dynamical simulation of the Heisenberg spin glass in three dimensions, J. Phys. Soc. Jpn. 60, 41–44 (1991)
22.46.
F. Matsubara, T. Iyota: Hybrid Monte-Carlo spin-dynamics simulation of short-range ± J Heisenberg models with and without anisotropy, Prog. Theor. Phys. 90, 471–498 (1993)
22.47.
S. Kirkpatrick, C. D. Gelatt, M. P. Vecchi: Optimization by simulated annealing, Science 220, 671–680 (1983)
22.48.
E. Marinari, G. Parisi: Simulated tempering: a new Monte Carlo scheme, Europhys. Lett. 19, 451–458 (1992)
22.49.
W. Kerler, P. Rehberg: Simulated-tempering procedure for spin-glass simulations, Phys. Rev. E 50, 4220–4225 (1994)
22.50.
K. Hukushima, K. Nemoto: Exchange Monte Carlo method and application to spin glass simulations, J. Phys. Soc. Jpn. 65, 1604–1608 (1996)
22.51.
R. H. Swendsen, J.-S. Wang: Replica Monte Carlo simulation of spin-glasses, Phys. Rev. Lett. 57, 2607–2609 (1986)
22.52.
J.-S. Wang, R. H. Swendsen: Replica Monte Carlo simulation (revisited), Prog. Theor. Phys. Suppl. 157, 317–323 (2005)
22.53.
M. Suzuki: Quantum Monte Carlo methods in Condensed Matter Physics, ed. by M. Suzuki (World Scientific, Singapore 1993)
22.54.
M. Suzuki: Relationship between d-dimensional quantal spin systems and (d+1)-dimensional Ising systems — equivalence, critical exponents and systematic approximants of the partition function and spin correlations —, Prog. Theor. Phys. 56, 1454–1469 (1976)
22.55.
M. Suzuki: Generalized Trotters formula and systematic approximants of exponential operators and inner derivations with applications to many-body problems, Comm. Math. Phys. 51, 183–190 (1976)
22.56.
M. Suzuki: General theory of higher-order decomposition of exponential operators and symplectic integrators, Phys. Lett. A 165, 387–395 (1992)
22.57.
M. Suzuki: General nonsymmetric higher-order decomposition of exponential operators and symplectic integrators, J. Phys. Soc. Jpn. 61, 3015–3019 (1992)
22.58.
J. E. Hirsch, R. L. Sugar, D. J. Scalapino, R. Blankenbecler: Monte Carlo simulations of one-dimensional fermion systems, Phys. Rev. B 26, 5033–5055 (1982)
22.59.
H. De Raedt, A. Lagendijk: Monte-Carlo simulation of quantum statistical lattice models, Phys. Report 127, 233–307 (1985)
22.60.
M. Suzuki: Quantum Monte Carlo Methods in Equilibrium and Nonequilibrium Systems, ed. by M. Suzuki (Springer, Berlin, Heidelberg 1987)
22.61.
M. Suzuki, S. Miyashita, A. Kuroda: Monte Carlo simulation of quantum spin systems I., Prog. Theor. Phys. 58, 1377–1387 (1977)
22.62.
T. Sakaguchi, K. Kubo, S. Takada: Monte Carlo simulation for the in-plane susceptibility of 1D spin 1/2 and 1 XY model, J. Phys. Soc. Jpn. 54, 861–864 (1985)
22.63.
S. Miyashita: Thermodynamic properties of spin 1/2 antiferromagnetic Heisenberg model on the square lattice, J. Phys. Soc. Jpn. 57, 1934–1946 (1988)
22.64.
M. Suzuki: Fractal decomposition of exponential operators with applications to many-body theories and Monte Carlo simulations, Phys. Lett. A 146, 319–323 (1990)
22.65.
M. Suzuki: General theory of fractal path integrals with applications to many-body theories and statistical physics, J. Math. Phys. 32, 400–407 (1991)
22.66.
H. G. Evertz: The loop algorithm, Adv. in Phys. 52, 1–66 (2003)
22.67.
N. Kawashima, K. Harada: Recent developments of world-line Monte Carlo methods, J. Phys. Soc. Jpn. 73, 1379–1414 (2004)
22.68.
N. Kawashima, J. E. Gubernatis: Dual Monte Carlo and cluster algorithms, Phys. Rev. E 51, 1547–1559 (1995)
22.69.
N. Kawashima, J. E. Gubernatis: Generalization of the Fortuin-Kasteleyn transformation and its application to quantum spin simulations, J. Stat. Phys. 80, 169–221 (1995)
22.70.
N. Kawashima: Cluster algorithms for anisotropic quantum spin models, J. Stat. Phys. 82, 131–153 (1996)
22.71.
N. Kawashima, J. E Gubernatis, H. G. Evertz: Loop algorithms for quantum simulations of fermion models on lattices, Phys. Rev. B 50, 136–149 (1994)
22.72.
B. B. Beard, U.-J. Wiese: Simulations of discrete quantum systems in continuous Euclidean time, Phys. Rev. Lett. 77, 5130–5133 (1996)
22.73.
N. Kawashima, J. E. Gubernatis: Loop algorithms for Monte Carlo simulations of quantum spin systems, Phys. Rev. Lett. 73, 1295–1298 (1994)
22.74.
S. Todo, K. Kato: Cluster algorithms for general-S quantum spin systems, Phys. Rev. Lett. 87, 047203(1–4) (2001)
22.75.
V. A. Kashurnikov, N. V. Prokofev, B. V. Svistunov, M. Troyer: Quantum spin chains in a magnetic field, Phys. Rev. B 59, 1162–1167 (1999)
22.76.
N. V. Prokov'ev, B. V. Svistunov, I. S. Tupitsyn: Exact, complete, and universal continuous-time worldline Monte Carlo approach to the statistics of discrete quantum systems, Sov. Phys. JETP 87, 310–321 (1998)
22.77.
N. V. Prokof'ev, B. V. Svistunov, I. S. Tupitsyn: “Worm” algorithm in quantum Monte Carlo simulations, Phys. Lett. A 238, 253–257 (1998)
22.78.
O.F. Syljuåsen, A. W. Sandvik: Quantum Monte Carlo with directed loops, Phys. Rev. E 66, 046701(1–28) (2002)
22.79.
A. W. Sandvik, J. Kurkijärvi: Quantum Monte Carlo simulation method for spin systems, Phys. Rev. B 43, 5950–5961 (1991)
22.80.
A. W. Sandvik: Generalization of Handscomb's quantum Monte-Carlo scheme - application to the 1D Hubbard-model, J. Phys. A 25, 3667–3682 (1992)
22.81.
A. W. Sandvik: Finite-size scaling of the ground-state parameters of the two-dimensional Heisenberg model, Phys. Rev. B 56, 11678–11690 (1997)
22.82.
A. W. Sandvik: Stochastic series expansion method with operator-loop update, Phys. Rev. B 59, R14157–R14160 (1999)
22.83.
J. E. Hirsch: Monte Carlo study of the two-dimensional Hubbard model, Phys. Rev. Lett. 51, 1900–1903 (1983)
22.84.
J. E. Hirsch: Two-dimensional Hubbard model: numerical simulation study, Phys. Rev. B 31, 4403–4419 (1985)
22.85.
S. R. White, D. J. Scalapino, R. L. Sugar, E. Y. Loh, J. E. Gubernatis, R. T. Scalettar: Numerical study of the two-dimensional Hubbard model, Phys. Rev. B 40, 506–516 (1989)
22.86.
M. Imada, Y. Hatsugai: Numerical studies on the Hubbard model and the t-J model in one- and two-dimensions, J. Phys. Soc. Jpn. 58, 3752–3780 (1989)
22.87.
J. E. Hirsch: Discrete Hubbard-Stratonovich transformation for fermion lattice models, Phys. Rev. B 28, 4059–4061 (1983)
22.88.
J. Kuti: Stochastic method for the numerical study of lattice fermions, Phys. Rev. Lett. 49, 183–186 (1982)
22.89.
R. Blankenbecler, R. L. Sugar: Projector Monte Carlo method, Phys. Rev. D 27, 1304–1311 (1983)
22.90.
Y. C. Chen, T. K. Lee: t-J model studied by the power Lanczos method, Phys. Rev. B 51, 6723–6726 (1995)
22.91.
S. Sorella: Green function Monte Carlo with stochastic reconfiguration, Phys. Rev. Lett. 80, 4558–4561 (1998)
22.92.
S. Sorella, L. Capriotti: Phys. Rev. B 61, 2599–2612 (2000)
22.93.
S. Sorella: Generalized Lanczos algorithm for variational quantum Monte Carlo, Phys. Rev. B 64, 024512(1–16) (2001)
22.94.
H. J. M. van Bemmel, D.F.B. ten Haaf, W. van Saarloos, J. M. J. van Leeuwen, G. An: Fixed-node quantum Monte Carlo method for lattice fermions, Phys. Rev. Lett. 72, 2442–2445 (1994)
22.95.
D.F.B. ten Haaf, H. J. M. van Bemmel, J. M. J. van Leeuwen, W. van Saarloos, D. M. Ceperley: Proof for an upper bound in fixed-node Monte Carlo for lattice fermions, Phys. Rev. B 51, 13039–13045 (1995)
22.96.
D. M. Ceperley, B. J. Alder: Ground state of the electron gas by a stochastic method, Phys. Rev. Lett. 45, 566–569 (1980)
22.97.
D. M. Ceperley, B. J. Alder: Quantum Monte-Carlo, Science 231, 555–560 (1986)
22.98.
T. Nakamura: Vanishing of the negative-sign problem of quantum Monte Carlo simulations in one-dimensional frustrated spin systems, Phys. Rev. B 57, R3197–R3200 (1998)
22.99.
S. Chandrasekharan, U.-J. Wiese: Meron-cluster solution of fermion sign problems, Phys. Rev. Lett. 83, 3116–3119 (1999)
22.100.
S. Chandrasekharan, J. Cox, J. C. Osborn, U.-J. Wiese: Meron-cluster approach to systems of strongly correlated electrons, Nucl. Phys. B 673, 405–436 (2003)
22.101.
C. Domb, M. S. Green: Phase Transitions and Critical Phenomena, Vol. 3, ed. by C. Domb, M. S. Green (Academic Press, London 1974)
22.102.
G. A. Baker, Jr.: Quantitative Theory of Critical Phenomena, ed. by G. A. Baker, Jr. (Academic Press, San Diego 1990)
22.103.
S. R. White: Density matrix formulation for quantum renormalization groups, Phys. Rev. Lett. 69, 2863–2866 (1992)
22.104.
S. R. White: Density-matrix algorithms for quantum renormalization groups, Phys. Rev. B 48, 10345–10356 (1993)
22.105.
T. Nishino: Density matrix renormalization group method for 2D classical models, J. Phys. Soc. Jpn. 64, 3598–3601 (1995)
22.106.
R. J. Bursill, T. Xiang, G. A. Gehring: The density matrix renormalization group for a quantum spin chain at non-zero temperature, J. Phys.: Condns. Matter 8, L583–L590 (1996)
22.107.
N. Shibata: Thermodynamics of the anisotropic Heisenberg chain calculated by the density matrix renormalization group method, J. Phys. Soc. Jpn. 66, 2221–2223 (1997)
22.108.
X. Wang, T. Xiang: Transfer-matrix density-matrix renormalization-group theory for thermodynamics of one-dimensional quantum systems, Phys. Rev. B 56, 5061–5064 (1997)
22.109.
K. Maisinger, U. Schollwöck: Thermodynamics of frustrated quantum spin chains, Phys. Rev. Lett. 81, 445–448 (1998)
22.110.
M. Imada, T. Kashima: Path-integral renormalization group method for numerical study of strongly correlated electron systems, J. Phys. Soc. Jpn. 69, 2723–2726 (2000)
22.111.
T. Kashima, M. Imada: Path-integral renormalization group method for numerical study on ground states of strongly correlated electronic systems, J. Phys. Soc. Jpn. 70, 2287–2299 (2001)
22.112.
M. Imada, T. Mizusaki: Quantum-number projection in the path-integral renormalization group method, Phys. Rev. B 69, 125110(1–10) (2004)
22.113.
T. Kashima, M. Imada: Magnetic and metal-insulator transitions through bandwidth control in two-dimensional Hubbard models with nearest and next-nearest neighbor transfers, J. Phys. Soc. Jpn. 70, 3052–3067 (2001)
22.114.
H. Morita, S Watanabe, M. Imada: Nonmagnetic insulating states near the Mott transitions on lattices with geometrical frustration and implications for κ-(ET)2Cu2(CN)3, J. Phys. Soc. Jpn. 71, 2109–2112 (2002)
22.115.
S. Watanabe, M. Imada: Precise determination of phase diagram for two-dimensional Hubbard model with filling- and bandwidth-control Mott transitions: grand-canonical path-integral renormalization group approach, J. Phys. Soc. Jpn. 73, 1251–1266 (2004)
22.116.
S.-C. Zhang: A Unified Theory Based on SO(5) Symmetry of Superconductivity and Antiferromagnetism, Science 275, 1089–1096 (1997)
22.117.
E. Demler, W. Hanke, S.-C. Zhang: SO(5) theory of antiferromagnetism and superconductivity, Rev. Mod. Phys. 76, 909–974 (2004)
22.118.
K.-S. Liu, M. E. Fisher, D. R. Nelson: Quantum Lattice Gas and the Existence of a Supersolid, J. Low. Temp. Phys. 10, 655–683 (1973)
22.119.
M. E. Fisher, D. R. Nelson: Spin Flop, Supersolids, and Bicritical and Tetracritical Points, Phys. Rev. Lett. 32, 1350–1353 (1974)
22.120.
D. R. Nelson, J. M. Kosterlitz, M. E. Fisher: Renormalization-Group Analysis of Bicritical and Tetracritical Points, Phys. Rev. Lett. 33, 813–817 (1974)
22.121.
D. R. Nelson, M. E. Fisher, J. M. Kosterlitz: Bicritical and tetracritical points in anisotropic antiferromagnetic systems, Phys. Rev. B 13, 412–432 (1976)
22.122.
A. Aharony: Comment on “ ”Bicritical and Tetracritical Phenomena and Scaling Properties of the SO(5) Theory, Phys. Rev. Lett. 88, 059703(1) (2002), and references therein
22.123.
X. Hu: Bicritical and Tetracritical Phenomena and Scaling Properties of the SO(5) Theory, Phys. Rev. Lett. 87 (2001)
22.124.
X. Hu: Bicritical phenomena and scalingproperties of O(5) model, Physica A 321, 71–80 (2003)
22.125.
E. Arrigoni, W. Hanke: Renormalized SO(5) Symmetry in Ladders with Next-Nearest-Neighbor Hopping, Phys. Rev. Lett. 82, 2115–2118 (1999)
22.126.
E. Arrigoni, W. Hanke: Critical properties of projected SO(5) models at finite temperatures, Phys. Rev. B 62, 11770–11777 (2000)
22.127.
X. Hu: Reply to “Comment on ‘Bicritical and tetracritical phenomena and scaling properties of the SO(5) theory’”, Phys. Rev. Lett. 88, 059704(1–4) (2002)
22.128.
P. Pfeuty, D. Jasnow, M. E. Fisher: Crossover scaling functions for exchange anisotropy, Phys. Rev. B 10, 2088–2112 (1974)
22.129.
X. Hu, T. Koyama, M. Tachiki: Phase Diagram of a Superconducting and Antiferromagnetic System with SO(5) Symmetry, Phys. Rev. Lett. 82, 2568–2571 (1999)
22.130.
A. A. Abrikosov: On the magnetic properties of superconductors of the second group, Zh. Eksp. Teor. Fiz. 32, 1442 (1957)
22.131.
A. A. Abrikosov: On the magnetic properties of superconductors of the second group, Sov. Phys. JETP 5, 1174–1182 (1957)
22.132.
G. Blatter, M. V. Feigelman, V. B. Geshkenbein, A. I. Larkin, V. M. Vinokur: Vortices in high-temperature superconductors, Rev. Mod. Phys. 66, 1125–1388 (1994)
22.133.
G. W. Crabtree, D. R. Nelson: Vortex Physics in High-Temperature Superconductors, Physics Today 50, 38–45 (1997)
22.134.
T. Nattermann, S. Scheidl: Vortex-glass phases in type-II superconductors, Adv. Phys. 49, 607–704 (2000)
22.135.
E. Brezin, D. R. Nelson, A. Thiaville: Fluctuation effects near H c2 in type-II superconductors, Phys. Rev. B 31, 7124–7132 (1985)
22.136.
Y.-H. Li, S. Teitel: Vortex-line-lattice melting, vortex-line cutting, and entanglement in model high-T c superconductors, Phys. Rev. Lett. 66, 3301–3304 (1991)
22.137.
R. E. Hetzel, A. Sudbø, D. A. Huse: First-order melting transition of an Abrikosov vortex lattice, Phys. Rev. Lett. 69, 518–521 (1992)
22.138.
P. G. de Gennes: Superconductivity of Metals and Alloys (Addison-Wesley, Redwood City, CA 1966) translated by P. A. Pincus
22.139.
W. E. Lawrence, S. Doniach: Proceedings of LT12, Tokyo, 1970, ed. by E. Kanda (Keigaku, Tokyo 1971)
22.140.
X. Hu, S. Miyashita, M. Tachiki: Simulation for the first-order vortex-lattice melting transition in high-T c superconductors, Physica (Amsterdam) 282-287C, 2057–2058 (1997)
22.141.
X. Hu, S. Miyashita, M. Tachiki: δ-Function Peak in the Specific Heat of High-Tc Superconductors: Monte Carlo Simulation, Phys.Rev. Lett. 79, 3498–3501 (1997)
22.142.
X. Hu, S. Miyashita, M. Tachiki: Monte Carlo simulation on the first-order melting transition of high-T c superconductors in ĉ, Phys. Rev. B 58, 3438–3445 (1998)
22.143.
S. Miyashita, H. Nishimori, A. Kuroda, M. Suzuki: Monte Carlo Simulation and Static and Dynamic Critical Behavior of the Plane Rotator Model, Prog. Theo. Phys. 60, 1669–1685 (1978)
22.144.
A. E. Koshelev: Point-like and line-like melting of the vortex lattice in the universal phase diagram of layered superconductors, Phys. Rev. B 56, 11201–11212 (1997)
22.145.
A. K. Nguyen, A. Sudbø: Phase coherence and the boson analogy of vortex liquids, Phys. Rev. B 58, 2802–2815 (1998)
22.146.
P. Olsson, S. Teitel: Correlation Lengths in the Vortex Line Liquid of a High-T c Superconductor, Phys. Rev. Lett. 82, 2183–2186 (1999)
22.147.
X. Hu, M. Tachiki: Possible Tricritical Point in Phase Diagrams of Interlayer Josephson-Vortex Systems in High-T c Superconductors, Phys. Rev. Lett. 85, 2577–2580 (2000)
22.148.
K. B. Efetov: Fluctuations in layered superconductors in a parallel magnetic field, Sov. Phys. JETP 49, 905–910 (1979)
22.149.
B. I. Ivlev, N. B. Kopnin, m. m. Slomaa: Vortex-lattice/vortex-liquid states in anisotropic high-T c superconductor, Phys. Rev. B 43, 2896–2902 (1991)
22.150.
B. I. Ivlev, N. B. Kopnin, V. L. Pokrovsky: Shear instability of a vortex lattice in layered superconductors, J. Low Temp. Phys. 80, 187 (1990)
22.151.
L. V. Mikheev, E. B. Kolomeisky: Melting of a flux-line fluid confined by CuO2 planes: Lindemann-criterion failure, Phys. Rev. B 43, 10431–10435 (1991)
22.152.
S. E. Korshunov, A. I. Larkin: Problem of Josephson-vortex- lattice melting in layered superconductors, Phys. Rev. B 46, 6395–6399 (1992)
22.153.
G. Blatte, B. I. Ivlev, J. Rhyner: Kosterlitz-Thouless transition in the smectic vortex state of a layered superconductor, Phys. Rev. Lett. 66, 2392–2395 (1991)
22.154.
L. Balents, D. R. Nelson: Fluctuations and Intrinsic Pinning in Layered Superconductors, Phys. Rev. Lett. 73, 2618–2621 (1994)
22.155.
L. Balents, D. R. Nelson: Quantum smectic and supersolid order in helium films and vortex arrays, Phys. Rev. B 52, 12951–12968 (1995)
22.156.
Y. Iye, S. Nakamura, T. Tamegai: Absence of Current Direction Dependence of The Resistive State of High Temperature Superconductors in Magnetic Fields, Physica 159C, 433–438 (1989)
22.157.
W. K. Kwok, U. Welp, G. W. Crabtree, K. G. Vandervoort, R. Hulscher, J. Z. Liu: Direct observation of dissipative flux motion and pinning by twin boundaries in YBa2Cu3O7−δ single crystals, Phys. Rev. Lett. 64, 966–969 (1990)
22.158.
W. K. Kwok, J. Fendrich, U. Welp, S. Fleshler, J. Downey, G. W. Crabtree: Suppression of the first order vortex melting transition by intrinsic pinning in YBa2Cu3O7−δ , Phys. Rev. Lett. 72, 1088–1091 (1994)
22.159.
X. Hu, M. Tachiki: Decoupled two-dimensional superconductivity and continuous melting transitions in layered superconductors immersed in a parallel magnetic field, Phys. Rev. B 70, 064506(1–13) (2004)
22.160.
X. Hu, M. Tachiki: Structure and Phase Transition of Josephson Vortices in Anisotropic High-T c Superconductors, Phys. Rev. Lett. 80, 4044–4047 (1998)
22.161.
X. Hu: Pinning Effects in Vortex States of High-T c Superconductors: Monte Carlo Simulations, J. Low. Temp. Phys. 131, 979–986 (2003)
22.162.
X. Hu, M.-B. Luo, Y.-Q. Ma: Density functional theory for freezing transition of vortex-line liquid with periodic layer pinning, Phys. Rev. B 72, 174503(1–6) (2005)
22.163.
A. I. Larkin: Effect of inhomogeneities on the structure of the mixed state of superconductors, Sov. Phys. JETP 31, 784–786 (1970)
22.164.
A. I. Larkin, Y. N. Ovchinnikov: Pinning in type II superconductors, J. Low Temp. Phys. 34, 409–428 (1979)
22.165.
Y. Imry, S.-K. Ma: Random-field instability of the ordered state of continuous symmetry, Phys. Rev. Lett. 35, 1399–1401 (1975)
22.166.
T. Nattermann: Scaling approach to pinning: Charge density waves and giant flux creep in superconductors, Phys. Rev. Lett. 64, 2454–2457 (1990)
22.167.
S. E. Korshunov: Replica symmetry breaking in vortex glasses, Phys. Rev. B 48, 3969–3975 (1993)
22.168.
T. Giamarchi, P. Le Doussal: Elastic theory of pinned flux lattices, Phys. Rev. Lett. 72, 1530–1533 (1994)
22.169.
T. Giamarchi, P. Le Doussal: Elastic theory of flux lattices in the presence of weak disorder, Phys. Rev. B 52, 1242–1270 (1995)
22.170.
T. Giamarchi, P. Le Doussal: Phase diagrams of flux lattices with disorder, Phys. Rev. B 55, 6577–6583 (1997)
22.171.
P. Olsson, S. Teitel: Disorder driven melting of the vortex line lattice, Phys. Rev. Lett. 87, 137001(1–4) (2001)
22.172.
Y. Nonomura, X. Hu: Effects of point defects on the phase diagram of vortex states in high− T c superconductors in the B ∥ c cxis, Phys. Rev. Lett. 86, 5140–5143 (2001)
22.173.
Y. Nonomura, X. Hu: Crossover behaviors in liquid region of vortex states above a critical point caused by point defects, cond-mat/0302597
22.174.
Y. Nonomura, X. Hu: Possible Bragg-Bose glass phase in vortex states of high-T c superconductors with sparse and weak columnar defects, Europhys. Lett. 65, 533–539 (2004)
22.175.
M. J. P. Gingras, D. A. Huse: Topological defects in the random-field XY model and the pinned vortex lattice to vortex glass transition in type-II superconductors, Phys. Rev. B 53, 15193–15200 (1996)
22.176.
S. Ryu, A. Kapitulnik, S. Doniach: Field-driven topological glass transition in a model flux line lattice, Phys. Rev. Lett. 77, 2300–2303 (1996)
22.177.
M. P. A. Fisher: Vortex-glass superconductivity: A possible new phase in bulk high-T c oxides, Phys. Rev. Lett. 62, 1415–1418 (1989)
22.178.
M. P. A. Fisher, D. S. Fisher, D. A. Huse: Thermal fluctuations, quenched disorder, phase transitions, and transport in type-II superconductors, Phys. Rev. B 43, 130–159 (1991)
22.179.
A. van Otterlo, R. T. Scalettar: Phase diagram of disordered vortices from London Langevin simulations, Phys. Rev. Lett. 81, 1497–1500 (1998)
22.180.
R. Sugano, T. Onogi, K. Hirata, M. Tachiki: The effect of pointlike pinning on vortex phase diagram of Bi2Sr2CaCu2O8+δ , Physica C 357-360, 428–431 (2001), and references therein
22.181.
A. Vestergren, J. Lidmar, M. Wallin: Vortex glass transition in a random pinning model, Phys. Rev. Lett. 88, 117004(1–4) (2002)
22.182.
P. Olsson: Vortex glass transition in a frustrated 3D XY model with disorder, Phys. Rev. Lett. 91, 077002(1–4) (2003)
22.183.
J. Lidmar: Amorphous vortex glass phase in strongly disordered superconductors, Phys. Rev. Lett. 91, 097001(1–4) (2003)
22.184.
F. O. Pfeiffer, H. Rieger: Numerical study of the strongly screened vortex-glass model in an external field, Phys. Rev. B 60, 6304–6307 (1999)
22.185.
H. Kawamura: Simulation studies on the stability of the vortex-glass order, J. Phys. Soc. Jpn. 69, 29–32 (2000)
22.186.
T. K. Worthington, M. P. A. Fisher, D. A. Huse, J. Toner, A. D. Marwick, T. Zabel, C. A. Feild, F. Holtzberg: Phys. Rev. B 46, 11854–11861 (1992)
22.187.
T. Nishizaki, K. Shibata, T. Sasaki, N. Kobayashi: New equilibrium phase diagram of YBa2Cu3O y under high magnetic fields, Physica C 341-348, 957–960 (2000)
22.188.
K. Shibata, T. Nishizaki, T. Sasaki, N. Kobayashi: Phase transition in the vortex liquid and the critical endpoint in YBa2Cu3O y , Phys. Rev. B 66, 214518(1–7) (2002)
22.189.
J. Kierfeld, V. Vinokur: Dislocations and the critical endpoint of the melting line of vortex line lattices, Phys. Rev. B 61, R14928–14931 (2000)
22.190.
G. P. Mikitik, E. H. Brandt: Effect of pinning on the vortex-lattice melting line in type-II superconductors, Phys. Rev. B 68, 054509(1–15) (2003)
22.191.
F. Bouquet, C. Marcenat, E. Steep, R. Calemczuk, W. K. Kwok, U. Welp, G. W. Crabtree, R. A. Fisher, N. E. Phillips, A. Schilling: An unusual phase transition to a second liquid vortex phase in the superconductor YBa2Cu3O7, Nature 411, 448–451 (2001)
22.192.
M. P. A. Fisher, P. B. Weichman, G. Grinstein, D. S. Fisher: Boson localization and the superfluid-insulator transition, Phys. Rev. B 40, 546–570 (1989)
22.193.
D. R. Nelson, V. M. Vinokur: Boson localization and pinning by correlated disorder in high-temperature superconductors, Phys. Rev. Lett. 68, 2398–2401 (1992)
22.194.
D. R. Nelson, V. M. Vinokur: Boson localization and correlated pinning of superconducting vortex arrays, Phys. Rev. B 48, 13060–13097 (1993)
22.195.
J. Lidmar, M. Wallin: Critical properties of Bose-glass superconductors, Europhys. Lett. 47, 494–500 (1999)
22.196.
L. Radzihovsky: Resurrection of the melting line in the Bose glass superconductor, Phys. Rev. Lett. 74, 4923–4926 (1995)
22.197.
T. Giamarchi, P. Le Doussal: Variational theory of elastic manifolds with correlated disorder and localization of interacting quantum particles, Phys. Rev. B 53, 15206–15225 (1996)
22.198.
C. Zeng, P. L. Leath, D. S. Fisher: Absence of two-dimensional Bragg glasses, Phys. Rev. Lett. 82, 1935–1938 (1999)
22.199.
S. Tyagi, Y. Y. Goldschmidt: Effects of columnar disorder on flux-lattice melting in high-temperature superconductors, Phys. Rev. B 67, 214501(1–15) (2003)
22.200.
C. Dasgupta, O. T. Valls: Two-step melting of the vortex solid in layered superconductors with random columnar pins, Phys. Rev. Lett. 91, 127002(1–4) (2003)
22.201.
C. Dasgupta, O. T. Valls: Melting and structure of the vortex solid in strongly anisotropic layered superconductors with random columnar pins, Phys. Rev. B 69, 214520(1–16) (2004)
22.202.
M. Kohno, M. Takahashi, M. Hagiwara: Low-temperature properties of the spin-1 antiferromagnetic Heisenberg chain with bond alternation, Phys. Rev. B 57, 1046–1051 (1998)
22.203.
F. D. M. Haldane: Nonlinear field theory of large-spin Heisenberg antiferromagnets: semiclassically quantized solitons of the one-dimensional easy-axis Néel state, Phys. Rev. Lett. 50, 1153–1156 (1983)
22.204.
F. D. M. Haldane: Continuum dynamics of the 1-D Heisenberg antiferromagnet: identification with the O(3) nonlinear sigma model, Phys. Lett. A 93, 464–468 (1983)
22.205.
M. P. Nightingale, H. W. Blöte: Gap of the linear spin-1 Heisenberg antiferromagnet: a Monte Carlo calculation, Phys. Rev. B 33, 659–661 (1986)
22.206.
M. Takahashi: Spin-correlation function of the S = 1 antiferromagnetic Heisenberg chain at T = 0, Phys. Rev. B 38, 5188–5191 (1988)
22.207.
Y. Kato, A. Tanaka: Numerical study of the S = 1 antiferromagnetic spin chain with bond alternation, J. Phys. Soc. Jpn. 63, 1277–1280 (1994)
22.208.
W. J. L. Buyers, R. M. Morra, R. L. Armstrong, M. J. Hogan, P. Gerlach, K. Hirakawa: Experimental evidence for the Haldane gap in a spin-1 nearly isotropic, antiferromagnetic chain, Phys. Rev. Lett. 56, 371–374 (1986)
22.209.
M. Steiner, K. Kakurai, J. K. Kjems, D. Petitgrand, R. Pynn: Inelastic neutron scattering studies on 1D near-Heisenberg antiferromagnets: a test of the Haldane conjecture, J. Appl. Phys. 61, 3953–3955 (1987)
22.210.
I. A. Zaliznyak, L. P. Regnault, D. Petitgrand: Neutron-scattering study of the dynamic spin correlations in CsNiCl3 above Néel ordering, Phys. Rev. B 50, 15824–15833 (1994)
22.211.
J. P. Renard, M. Verdaguer, L. P. Regnault, W. A. C. Erkelens, J. Rossat-Mignod, W. G. Stirling: Presumption for a quantum energy-gap in the quasi one-dimensional S = 1 Heisenberg-antiferromagnet Ni(C2H8N2)2NO2(ClO4), Europhys. Lett. 3, 945–951 (1987)
22.212.
I. Affleck: The quantum Hall-effects, σ-models at θ=π and quantum spin chains, Nucl. Phys. B 257, 397–406 (1985)
22.213.
I. Affleck: Exact critical exponents for quantum spin chains, nonlinear σ-models at θ=π and the quantum Hall-effect, Nucl. Phys. B 265, 409–447 (1986)
22.214.
I. Affleck, F. D. M.  Haldane: Critical theory of quantum spin chains, Phys. Rev. B 36, 5291–5300 (1987)
22.215.
E. Coronado, M. Drillon, A. Fuertes, D. Beltran, A. Mosset, J. Galy: Structural and magnetic study of Ni2(EDTA)(H2O)4,2H2O - alternating Landé factors in a two-sublattice 1D system, J. Am. Chem. Soc. 108, 900–905 (1986)
22.216.
R. Vicente, A. Escuer, J. Ribas, X. Solans: The first nickel(II) alternating chain with two different end-to-end azido bridges, Inorg. Chem. 31, 1726–1728 (1992)
22.217.
A. Escuer, R. Vicente, J. Ribas, M. S. E. Fallah, X. Solans, M. Font-Badría: Crystal structure and magnetic properties of trans-[Ni(333-tet)(μ-N3)] n (ClO4) n and cis-[Ni(333-tet)(μ-(N3))] n (PF6) n : two novel kinds of structural nickel(II) chains with a single azido bridge. Magnetic behavior of an alternating S=1 chain with α=0.46, Inorg. Chem. 33, 1842–1847 (1994)
22.218.
J. J. Borrás-Almenar, E. Coronado, J. Curely, R. Georges: Exchange alternation and single-ion anisotropy in the antiferromagnetic Heisenberg chain S=1. Magnetic and thermal properties of the compound Ni2(EDTA)⋅6H2O, Inorg. Chem. 34, 2699–2704 (1995)
22.219.
A. Escuer, R.  Vicente, X. Solans, M. Font-Badría: Crystal structure and magnetic properties of [Ni2(dpt)2(μ-ox)(μ-N3) n ](PF6) n : a new strategy to obtain S=1 alternating chains, Inorg. Chem. 33, 6007–6011 (1994)
22.220.
M. Hagiwara, Y. Narumi, K. Kindo, M. Kohno, H. Nakano, R. Sata, M. Takahashi: Experimental verification of the gapless point in the S=1 antiferromagnetic bond alternating chain, Phys. Rev. Lett. 80, 1312–1315 (1998)
22.221.
O. A. Starykh, R. R. P. Singh, A. W. Sandvik: Quantum critical scaling and temperature-dependent logarithmic corrections in the spin-half Heisenberg chain, Phys. Rev. Lett. 78, 539–542 (1997)
22.222.
O. A. Starykh, A. W. Sandvik, R. R. P. Singh: Dynamics of the spin-1/2 Heisenberg chain at intermediate temperatures, Phys. Rev. B 55, 14953–14967 (1997)
22.223.
N. Furukawa, M. Imada: Two-dimensional Hubbard model – metal insulator transition studied by Monte Carlo calculation –, J. Phys. Soc. Jpn. 61, 3331–3354 (1992)
22.224.
A. Ino, T. Mizokawa, A. Fujimori, K. Tamasaku, H. Eisaki, S. Uchida, T. Kimura, T. Sasagawa, K. Kishio: Chemical potential shift in overdoped and underdoped La2-xSrxCuO4, Phys. Rev. Lett. 79, 2101–2104 (1997)
22.225.
N. Harima, A. Fujimori, T. Sugaya, I. Terasaki: Chemical potential shift in lightly doped to overdoped Bi2Sr2Ca1−x R x Cu2O8+y (R=Pr, Er), Phys. Rev. B 67, 172501(1–4) (2003)
22.226.
R. J. Birgeneau, D. R. Gabbe, H. P. Jenssen, M. A. Kastner, P. J. Picone, T. R. Thurston, G. Shirane, Y. Endoh, M. Sato, K. Yamada, Y. Hidaka, M. Oda, Y. Enomoto, M. Suzuki, T. Murakami: Antiferromagnetic spin correlations in insulating, metallic, and superconducting La2−x Sr x CuO4, Phys. Rev. B 38, 6614–6623 (1988)
22.227.
M. Kohno: Ground-state properties of the two-dimensional t-J model, Phys. Rev. B 55, 1435–1441 (1997)
22.228.
M. Kohno, M. Takahashi: Magnetization process of the spin-1/2 XXZ models on square and cubic lattices, Phys. Rev. B 56, 3212–3217 (1997)
22.229.
V. J. Emery, S. A. Kivelson, H. Q. Lin: Phase separation in the t-J model, Phys. Rev. Lett. 64, 475–478 (1990)
22.230.
W. O. Putikka, M. U. Luchini, T. M. Rice: Aspects of the phase diagram of the two-dimensional t-J model, Phys. Rev. Lett. 68, 538–541 (1992)
22.231.
W. O. Putikka, M. U. Luchini: Limits on phase separation for two-dimensional strongly correlated electrons, Phys. Rev. B 62, 1684–1687 (2000)
22.232.
P. Prelovšek, X. Zotos: Hole pairing and clustering in the two-dimensional t-J model, Phys. Rev. B 47, 5984–5991 (1993)
22.233.
E. Dagotto, J. Riera, Y. C. Chen, A. Moreo, A. Nazarenko, F. Alcaraz, F. Ortolani: Superconductivity near phase separation in models of correlated electrons, Phys. Rev. B 49, 3548–3565 (1994)
22.234.
J. Jaklič, P. Prelovšek: Thermodynamic properties of the planar t-J model, Phys. Rev. Lett. 77, 892–895 (1996)
22.235.
C. S. Hellberg, E. Manousakis: Phase separation at all interaction strengths in the t-J model, Phys. Rev. Lett. 78, 4609–4612 (1997)
22.236.
C. S. Hellberg, E. Manousakis: Green's-function Monte Carlo for lattice fermions: application to the t-J model, Phys. Rev. B 61, 11787–11806 (2000)
22.237.
S. R. White, D. J. Scalapino: Density matrix renormalization group study of the striped phase in the 2D t-J model, Phys. Rev. Lett. 81, 1272–1275 (1998)
22.238.
S. R. White, D. J. Scalapino: Energetics of domain walls in the 2D t-J model, Phys. Rev. Lett. 81, 3227–3230 (1998)
22.239.
C. T. Shih, Y. C. Chen, T. K. Lee: Revisit phase separation of the two-dimensional t-J model by the power-Lanczos method, J. Phys. Chem. Sol. 62, 1797–1811 (2001)
22.240.
J. D. Cloizeaux, M. Gaudin: Anisotropic linear magnetic chain, J. Math. Phys. (N.Y.) 7, 1384–1400 (1966)
Metadaten
Titel
Monte Carlo Simulation
verfasst von
Xiao Hu, Associate Professor
Yoshihiko Nonomura, Ph.D.
Masanori Kohno, Dr.
Copyright-Jahr
2006
Buch
Springer Handbook of Materials Measurement Methods

Print ISBN: 978-3-540-20785-6

Electronic ISBN: 978-3-540-30300-8

Copyright-Jahr: 2006

DOI
https://doi.org/10.1007/978-3-540-30300-8_22

Premium Partner

    Marktübersichten

    Die im Laufe eines Jahres in der „adhäsion“ veröffentlichten Marktübersichten helfen Anwendern verschiedenster Branchen, sich einen gezielten Überblick über Lieferantenangebote zu verschaffen. 

    Zur Marktübersicht
    Bildnachweise