THE EQUIVALENCE OF ENSEMBLES FOR LATTICE SYSTEMS - SOME EXAMPLES AND A COUNTEREXAMPLE

We describe the problem of the equivalence of ensembles at the level o f states for classical lattice systems. We discuss circumstances where the vanishing of the specific information gain of a sequence of micro canonical measures with respect to a sequence of grand canonical measu res implies the equivalence of ensembles. We give a simple derivation of a criterion for the vanishing of the specific information gain in t erms of thermodynamic functions. The proof uses ideas From the theory of large deviations but is self-contained. We show how the criterion w orks in a simple model of a paramagnet and in the Ising model of a fer romagnet in any dimension but fails in the case of the Curie-Weiss mea n-field model.