A Priori Estimates for Symmetrizing Measures and Their Applications to Gibbs States

We prove existence and uniform a priori estimates for tempered Gibbs states of certain classical lattice systems with unbounded spins, nonharmonic pair potentials, and infinite radius of interaction. We use an alternative characterization of Gibbs measures in terms of their Radon–Nikodym derivatives w.r.t. local shifts of the configuration space and corresponding integration by parts formulas.