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

We consider zero-temperature, stochastic Ising models sigma(t) with nearest -neighbor interactions and an initial spin configuration sigma(0) chosen fr om a symmetric Bernoulli distribution (corresponding physically to a deep q uench). Whether sigma(infinity) exists, i.e., whether each spin flips only finitely many times as t --> infinity (for almost every sigma(0) and realiz ation 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 t he couplings, the dimension, and the lattice type. We review results, exami ne open questions, and discuss related topics. (C) 2000 Elsevier Science B. V. All rights reserved.