Multiple Domain Growth and Memory in the Droplet Model for Spin-Glasses

Abstract

We study domain growth dynamics when the target state is suddenly changed on all length scales. This procedure mimics the `chaos' effect postulated by the droplet theory of spin-glasses, and allows us to investigate in details its various dynamical consequences. We study the problem by a variety of methods, including scaling arguments, analytical solution of the spherical Mattis model, and Monte Carlo simulations of a 2-dimensional Ising Mattis model. We show that successive coarsening with respect to different equilibrium states imprints multiple domain structures on top of each other, plus extra noise due to random interferences. We demonstrate that the domain structures can be retrieved by an additional series of coarsening in the reversed order which removes the noises. We discuss the rejuvenation (chaos) and memory effects observed in temperature-cycling experiments in glassy systems from the present point of view, and discuss some open problems and alternative descriptions.