Equilibration of random-field Ising systems

Abstract

The equilibration of Ising systems in random magnetic fields at low temperatures (T) following a quench from high T is studied in the framework of a simple solid-on-solid model. The rate at which ordered domains in the model grow with time in any dimension (d) is estimated as a function of the random-field strength, the exchange strength, and T, on the basis of an approximate analogy to the problem of a one-dimensional random walk in a random medium. Domains are argued to grow logarithmically with time for all d. This result has a simple interpretation in terms of energy barriers which must be surmounted in the equilibration process. © 1984 The American Physical Society.