Comparison of Finite Volume Canonical and Grand Canonical Gibbs Measures under a Mixing Condition

#### N. Cancrini, F. Martinelli

2000, v.6, Issue 1, 23-72

ABSTRACT

We envisage a simple approach to prove sharp bounds between the finite volume (multi) canonical and (multi) grand canonical expectation of local observables of a lattice discrete spin model by assuming a mixing property for the Gibbsian specifications. We then apply our results to various situations including mean field perturbations of the Ising model. Our method does not rely upon a local limit theorem and applies also to the dilute Ising model in the Griffiths phase for which the mixing condition fails.

Keywords: Gibbs measures,equivalence of ensembles,Gibbs conditioning principle