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

Using the formalism and the results described in [QMPS I] and in [QMPS III], we discuss the approach to termodynamic equilibrium for discrete spin systems in a framework that generalizes the one originally proposed by R. Glauber. Ergodicity for the process is proved by providing a lower bound extimate for their exponetial rate of convergence to equilibrium, in the high temperature regime. We give application to some (not necessarily ferromagnetic ) Ising-spin models. These results also gives an upper bound for the critical temperature of the d-dimensional Ising model, which in dimension two coincides with the real critical value calculated by the static approach.