A.C.D. van Enter, B. Zegarlinski
A Remark on the Differentiability of the Pressure Functional
(63K, TeX)
ABSTRACT. We give a short review of results on equilibrium description and
description by stochastic dynamics for spin systems on a lattice.
We remark also that some coercive inequalities for the generators
of stochastic dynamics, as e.g. the Logarithmic Sobolev inequality,
can be used in a direct and natural way to prove
strong differentiability properties of the pressure functional
for lattice spin systems with multiparticle interactions at high temperatures.
Motivated by this, we exhibit also a class of examples of multiparticle
interactions which do not belong to the space $\B2$ of spin interactions,
but for which the Gibbs measures exist and are unique at high temperatures.