Log-Sobolev Inequalities for Infinite-Dimensional Gibbs Measures with Non-Quadratic Interactions

J. Inglis, I. Papageorgiou

2019, v.25, Issue 5, 879-898

ABSTRACT

We focus on the log-Sobolev inequality for spin systems on the lattice with interactions of higher order than quadratic.
We show that if the one-dimensional single-site measure with boundaries
satisfies the log-Sobolev inequality uniformly in the boundary conditions
then the infinite-dimensional Gibbs measure also satisfies the inequality
under appropriate conditions on the phase and the interactions. Our result can be applied to spin spaces being nilpotent Lie groups on $\R^n$.

Keywords: log-Sobolev inequality, Gibbs measure, spin systems