Zero-temperature dynamics of Ising spin systems following a deep quench: results and open problems

Abstract

We consider zero-temperature, stochastic Ising models σ t with nearest-neighbor interactions and an initial spin configuration σ 0 chosen from a symmetric Bernoulli distribution (corresponding physically to a deep quench). Whether σ ∞ exists, i.e., whether each spin flips only finitely many times as t→∞ (for almost every σ 0 and realization of the dynamics), or if not, whether every spin — or only a fraction strictly less than one — flips infinitely often, depends on the nature of the couplings, the dimension, and the lattice type. We review results, examine open questions, and discuss related topics.