Communications in Mathematical Physics

, Volume 31, Issue 4, pp 291–294 | Cite as

A continuity property of the entropy density for spin lattice systems

  • M. Fannes


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.


Entropy Neural Network Statistical Physic Complex System Nonlinear Dynamics 
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    Kato, T.: Perturbation theory for linear operators. Theorem III.6.10. Berlin-Heidelberg-New York: Springer 1966.Google Scholar

Copyright information

© Springer-Verlag 1973

Authors and Affiliations

  • M. Fannes
    • 1
    • 2
  1. 1.Universiteit LeuvenBelgium
  2. 2.Dept. Nat. Celestijnenlaan 200 DInstituut voor theoretische fysicaHeverleeBelgium

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