 97649 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 semiclassical 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
singlespin phase and when the nearest neighbor interaction is small
enough.
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