An introduction to metastability through random walks
The paper is a guide for beginners into the metastability problem which is a dynamical phenomenon taking place in the vicinity of a first order phase transition in a lattice spin system. The physical motivation is that of a ferromagnetic behavior. Its formal implementation is given in terms of the Ising model, with emphasis on Glauber and Kawasaki modifications of the original model. The principal aim of the authors is to describe the evolution of a metastable state and its decay to the stable equilibrium through the nucleation to the stable phase. Major mathematical techniques come from the Wentzell-Freidlin theory of small random perturbations of dynamical systems and also involve analytical methods to control the convergence to equilibrium of a random process, by means of the spectral properties of its generator.
scientific article; zbMATH DE number 5764987
scientific article