Demagnetization via Nucleation of the Nonequilibrium Metastable Phase in a Model of Disorder

We study both analytically and numerically demagnetization via nucleation of the metastable phase in a two–dimensional nonequilibrium Ising ferromagnet at temperature T . Canonical equilibrium is dynamically impeded by a weak random perturbation which models homogeneous disorder of undetermined source. We present a simple theoretical description, in perfect agreement with Monte Carlo simulations, assuming that the decay of the nonequilibrium metastable state is due, as in equilibrium, to the competition between the surface and the bulk. This suggests one to accept a nonequilibrium free–energy at a mesoscopic/cluster level, and it ensues a nonequilibrium surface tension with some peculiar low–T behavior. We illustrate the occurrence of intriguing nonequilibrium phenomena, including: (i) stochastic resonance phenomena at low T which stabilize the metastable state as temperature increases; (ii) reentrance of the limit of metastability under strong nonequilibrium conditions; and (iii) noise–enhanced propagation of domain walls. The cooperative behavior of our system, which is associated to the interplay between thermal and nonequilibrium fluctuations, may also be understood in terms of a Langevin equation with additive and multiplicative noises. We also studied metastability in the case of open boundaries as it may correspond to a magnetic nanoparticle. We then observe the most irregular relaxation triggered by the additional surface randomness. In particular, at low T, the relaxation becomes discontinuous as occurring by way of scale–free avalanches, so that it resembles the type of relaxation reported for many complex systems. We show that this results from the superposition of many demagnetization events, each with a well–defined scale which is determined by the curvature of the domain wall at which it originates. This is an example of (apparent) scale invariance in a nonequilibrium setting which is not to be associated with any familiar kind of criticality.