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A continuity property of the entropy density for spin lattice systems

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Abstract

The entropy density of spin lattice systems is known to be a weak upper semi-continuous functional on the set of the lattice invariant states. (It is even weak discontinuous.) However we prove here that it is continuous with respect to the norm topology on those states.

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References

  1. Lanford, O., Robinson, D.W.: J. Math. Phys.9, 1120 (1968).

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  2. Fannes, M.: The entropy density of quasi free states, Preprint July 1972 KUL Leuven Belgium.

  3. Kato, T.: Perturbation theory for linear operators. Theorem III.6.10. Berlin-Heidelberg-New York: Springer 1966.

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Authors and Affiliations

  1. Universiteit Leuven, Belgium

    M. Fannes

  2. Dept. Nat. Celestijnenlaan 200 D, Instituut voor theoretische fysica, B-3030, Heverlee, Belgium

    M. Fannes

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  1. M. Fannes
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Aspirant van het Belgisch N.F.W.O.

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Fannes, M. A continuity property of the entropy density for spin lattice systems. Commun.Math. Phys. 31, 291–294 (1973). https://doi.org/10.1007/BF01646490

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  • DOI: https://doi.org/10.1007/BF01646490

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