On the Metastability in Three Modifications of the Ising Model

摘要

We consider three extensions of the standard 2D Ising model with Glauber dynamics on a finite torus at low temperature. The first model (see Chapter 2) is an anisotropic version, where the interaction energy takes different values on vertical and on horizontal bonds. The second model (Chapter 3) adds next-nearest-neighbor attraction to the standard Ising model. And the third model (Chapter 4) associates different alternating signs for the magnetic fields on even and odd rows. All these models have already been studied, and results concerning metastability have been established using the so-called path-wise approach (see [11], [12], [14]). In this text, we extend these earlier results, and apply the potential-theoretic approach to metastability to obtain more precise asymptotic information on the transition time from the metastable phase to the stable phase.