Log-Sobolev inequalities for infinite-dimensional Gibbs measures with   non-quadratic interactions
  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. 
James Inglis and Ioannis Papageorgiou (Sao Paulo)
math.FA