Helffer B.
Remarks on decay of correlations and Witten Laplacians III\\
--Applications to logarithmic Sobolev inequalities--
(40K, LATEX)
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.