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


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.


Neural Network Statistical Physic Correlation Function Complex System Nonlinear Dynamics 
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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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