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Communications in Mathematical Physics

, Volume 101, Issue 2, pp 153–172 | Cite as

Discrete lattice systems and the equivalence of microcanonical, canonical and grand canonical Gibbs states

  • Paul Vanheuverzwijn
Article

Abstract

It is proven that a microcanonical Gibbs measure on a classical discrete lattice system is a mixture of canonical Gibbs measures, provided the potential is “approximately periodic,” has finite range and possesses a commensurability property. No periodicity is imposed on the measure. When the potential is not approximately periodic or does not have the commensurability property, the inclusion does not hold.

As a by-product, a new proof is given of the fact that for a large class of potentials, a canonical Gibbs measure is a mixture of grand canonical measures. Thus the equivalence of ensembles is obtained in the sense of identical correlation functions.

Keywords

Neural Network Statistical Physic Correlation Function Complex System Nonlinear Dynamics 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag 1985

Authors and Affiliations

  • Paul Vanheuverzwijn
    • 1
  1. 1.Instituut voor Theoretische FysicaUniversiteit LeuvenLeuvenBelgium

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