The log-Sobolev inequality for weakly coupled lattice fields

Abstract We consider a ferromagnetic spin system with unbounded interactions on the d-dimensional integer lattice (d is arbitrary). Under mild assumptions on the one-body interactions (so that arbitrarily deep double wells are allowed), we prove that if the coupling constants are small enough, then the finite volume Gibbs states satisfy the log-Sobolev inequality uniformly in the volume and the boundary condition.