Quantum Methods for Interacting Particle Systems II, Glauber Dynamics for Ising Spin Systems

Using the formalism and the results described in [I] and in [Gi], we discuss the approach to termodynamic equilibrium for discrete spin systems in a framework that generalizes the one originally proposed by R. Glauber. We prove a lower bound extimate for their exponetial rate of convergence to equilibrium, in the high temperature regime which is better than those previously known. (the case of d = 1 is amenable to a more detailed analysis, see [MT]). We also give application to some (not necessarily ferromagnetic) Ising-spin models. These results provide an upper bound for the critical temperature of the d-dimensional Ising model.