Rapid Convergence to Equilibrium in One Dimensional Stochastic Ising Models

Abstract

We consider one dimensional stochastic Ising models with finite range interactions. For such processes we first prove that the semi-group of the process converges exponentially fast on the $L^2$ space of the Gibbs states. Under the additional hypothesis that the flip rates are attractive, we prove that the semigroup acting on the cylinder functions converges to equilibrium exponentially fast in the uniform norm.