Abstract
We develop a detailed finite-size-scaling theory at a general, asymmetric, temperature-driven, strongly first-order phase transition in a system with periodic boundary conditions. We compute scaling functions for various cumulants of energy in the form U(L,t)=()+() with t=1-/T. In particular, we consider the specific heat and Binder’s fourth cumulant and show this has a minimum value of 2/3-(/-//12+O() at a temperature (L)-=O(). Various other pseudocritical temperatures corresponding to extrema of other cumulants are evaluated. We compare these theoretical predictions with extensive Monte Carlo simulations of the nominally strong first-order transitions in the eight- and ten-state Potts models in two dimensions for system sizes L≤50. The ten-state simulations agree with theory in all details in contrast to the eight-state data, and we give estimates for the bulk specific heats at using all exactly known analytic results. A criterion is developed to estimate numerically whether or not system sizes used in a simulation of a first-order transition are in the finite-size-scaling regime.
- Received 11 June 1990
DOI:https://doi.org/10.1103/PhysRevB.43.3265
©1991 American Physical Society