94-362 A.C.D. van Enter, B. Zegarlinski

A Remark on the Differentiability of the Pressure Functional (63K, TeX) Nov 22, 94

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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.

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