93-21 F.Martinelli , E.Olivieri

APPROACH TO EQUILIBRIUM OF GLAUBER DYNAMICS IN THE ONE PHASE REGION II. THE GENERAL CASE (81K, plain TeX) Jan 26, 93

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Abstract. We develop a new method, based on renormalization group ideas (block decimation procedure), to prove, under an assumption of strong mixing in a finite cube $\Lambda_o$, a Logarithmic Sobolev Inequality for the Gibbs state of a discrete spin system. As a consequence we derive the hypercontractivity of the Markov semigroup of the associated Glauber dynamics and the exponential convergence to equilibrium in the uniform norm in all volumes $\Lambda$ "multiples" of the cube $\Lambda_o$.

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