97-649 Helffer B.
Remarks on decay of correlations and Witten Laplacians III\\ --Applications to logarithmic Sobolev inequalities-- (40K, LATEX) Dec 26, 97
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Abstract. This is the continuation of our two previous articles devoted to the use of Witten Laplacians for analyzing Laplace integrals in statistical mechanics. The main application treated in Part I was a semi-classical one. The second application was more perturbative in spirit and gave very explicit estimates for the lower bound of the Witten Laplacian in the case of a quartic model. We shall relate in this third part our studies of the Witten Laplacian with the existence of uniform logarithmic Sobolev inequalities through a criterion of B. Zegarlinski. More precisely, our main contribution is to show how to control the decay of correlations uniformly with respect to various parameters, under a natural condition of strict convexity at $\infty$ of the single-spin phase and when the nearest neighbor interaction is small enough.

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