Uniqueness of Gibbs states for quantum lattice systems

Abstract

We prove uniqueness of Euclidean Gibbs states for certain quantum lattice systems with unbounded spins. We use Dobrushin’s uniqueness criterion. The necessary estimates for the Vasershtein distance between the corresponding one-point conditional distributions with boundary conditions differing only at one side, are obtained by proving a Log-Sobolev inequality on the infinite dimensional single spin (= loop) spaces. Some important classes of concrete examples to which all this applies are discussed.