Comparative Monte Carlo and mean-field studies of random-field Ising systems.

Abstract

Site-dependent mean-field theory and Monte Carlo (MC) simulations are used to study and compare random-field Ising ferromagnets (RFIM) and Ising diluted antiferromagnets in a field (DAFF). For short-time-scale simulations the two approaches lead to similar results for the various history-dependent magnetizations, and specific heats and for the metastable ground-state spin configurations. The results are also in reasonable qualitative accord with experiment. Mean-field theory which more readily provides information about free energies is used to compute the phase diagram for two- and three-dimensional random-field systems. Since thermal fluctuations are not important in the equilibrium critical behavior a mean-field approach is expected to contain much of the essential physics. At T=0, MC simulations corroborate the mean-field results. We distinguish three characteristic field-dependent temperatures which in order of decreasing magnitude are the irreversibility temperature ${T}_{\mathrm{irr}}$, the ordering temperature (${T}_{c}$ or ${T}_{N}$), and the temperature for stability of long-range order (LRO), ${T}_{s}$. ${T}_{\mathrm{irr}}$ corresponds to the temperature at which the free-energy surface first develops multiple minima.At an even lower temperature, ${T}_{c}$ or ${T}_{N}$, the metastable LRO minimum first appears. However, the LRO state is not the deepest minimum until the stability temperature ${T}_{s}$ is reached. In the two-dimensional (2D) RFIM, the zero-temperature intercept of ${T}_{s}$, called ${\ensuremath{\Delta}}_{c}$, scales to zero with the system size. This result, which is derived in mean-field theory and substantiated in MC, provides strong numerical evidence for the absence of stable LRO in 2D. We find that this 2D behavior is reflected in 3D by the metastability of LRO for a narrow range of T near the ordering temperature. This implies that the LRO state should exhibit time-dependent properties, near ${T}_{N}$ as has been reported recently. Furthermore, in equilibrium, the transition to the LRO state may be first order. The effects of H=0 disorder in the DAFF lead to different behavior in field hysteresis studies than in the RFIM. This result which is a consequence of the extremely anisotropic Ising limit suggests that theoretical predictions for the time-dependent properties of the RFIM may not be applicable to the experimentally realizable DAFF.