04-107 F. Baffioni, T. Kuna, I. Merola, E. Presutti

A relativized Dobrushin uniqueness condition and applications to Pirogov-Sinai models (594K, pdf) Apr 13, 04

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Abstract. The paper is divided in three parts: in part 1, we establish a Dobrushin like criterion for uniqueness of DLR measures, in a relatively abstract and general context. In part 2 we show that in "generalized" Pirogov-Sinai models the finite volume corrections to the pressure can be reduced to the analysis of restricted ensembles which naturally fit in the general scheme of Part 1. In Part 3 we apply the previous theory to systems with Kac potentials, namely the ferromagnetic Ising spins, the LMP models of particles in the continuum, [14], and their quantum version in the Ginibre loops representation. Our results on the latter are used in a companion paper, [1], to prove phase transitions.

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