A priori estimates for symmetrizing measures and their applications to Gibbs states (Q1975485)

The authors prove existence and uniform a priori estimates for tempered Gibbs states of certain classical lattice systems with unbounded spins, non-harmonic pair potentials, and infinite radius of interaction. In particular, multi-body interactions, not covered by previous work in this direction, are included. The techniques are based on an alternative characterization of Gibbs measures in terms of their Radon-Nikodým derivatives with respect to local shifts of the configuration space, and corresponding integration by parts formulas. This approach gives a characterization of Gibbs measures as the solution of an infinite system of first-order partial differential equations in infinitely many variables, which yields uniform a priori estimates by the methods known from finite-dimensional partial differential equations.