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 Λ0, 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 Λ “multiples” of the cube Λ0.
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Communicated by M. Aizenman
Work partially supported by grant SC1-CT91-0695 of the Commission of European Communities
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Martinelli, F., Olivieri, E. Approach to equilibrium of Glauber dynamics in the one phase region. Commun.Math. Phys. 161, 487–514 (1994). https://doi.org/10.1007/BF02101930
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DOI: https://doi.org/10.1007/BF02101930