98-545 F.Martinelli

An Elementary Approach to Finite Size Conditions for the Exponential Decay of Covariances in Lattice Spin Models (167K, postscript) Jul 29, 98

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Abstract. We consider lattice spin models with finite range interaction and compact spin space. Using the Markov property we derive in an elementary way, very much close to Lieb--Simon type of argument, finite size conditions for the exponential decay of finite volume covariances. Our method covers at the same time the case of completely analytical Gibbsian random fields introduced by Dobrushin and Shlosman for which covariances between local observables decay exponentially fast in any volume, and the case of Gibbsian random fields for which the decay of covariances is proved only on regular (e.g. cubic) volumes

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