T. Bodineau and B. Helffer
Correlations, Spectral gap and Log-Sobolev inequalities for 
unbounded spins systems.
(255K, Postscript)

ABSTRACT.  In this article, we would like to review recent results concerning 
the links between the decay of correlations, the spectral gap and 
the Log-Sobolev inequalities. 
This was motivated by various papers by Antoniouk&Antoniouk, 
Zegarlinski and Yoshida. We are mainly reporting on contributions 
by Helffer-Sj\"ostrand, Helffer, Yoshida and Bodineau-Helffer but 
also present some new results.