F.Martinelli , E.Olivieri
APPROACH TO EQUILIBRIUM OF GLAUBER DYNAMICS IN THE ONE PHASE REGION II.
THE GENERAL CASE
(81K, plain TeX)
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 $\Lambda_o$, 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 $\Lambda$ "multiples" of the cube $\Lambda_o$.