Irreversibility and metastability in spin-glasses. I. Ising model

Abstract

By studying the evolution (with field $H$ and temperature $T$) of the free-energy surface, we numerically calculate various history-dependent magnetizations. The interactions are assumed to be of short range with a Gaussian probability distribution. In this paper, only Ising spin-glasses are discussed. In a companion paper, we treat vector spins. Only the simplest mean-field (MF) approximation to the free-energy functional $F\left[\right\{m_i\left\}\right]$ (where $m_i$ is the thermally averaged spin at the ith site) is studied. For finite-size systems, it is difficult to include the reaction corrections to $F$ within a self-consistent formalism. Good qualitative agreement with experiment is found for the $T$ and $H$ dependence of the field-cooled and zero-field-cooled, and thermal and isothermal remanent magnetizations. Our hysteresis loops are qualitatively similar to those observed in AuFe spin-glasses. The characteristic changes in the shape of the loop as the Fe concentration increases can also be reproduced theoretically. At $T=0\mathrm{}$, the corrections to MF theory are negligible and it is shown that the ground states generated iteratively by cooling solutions of the MF equations are obtained much more rapidly and are of lower energy than those found in Monte Carlo simulations. It is demonstrated that the field-cooled state, which is obtained by a series of reversible procedures, is one for which linear-response theory (properly interpreted) and Maxwell's relations all hold. The close correspondence between our theory and experiment supports the hypothesis that on intermediate-time scales the behavior of spin-glasses is primarily determined by the properties of the free-energy surface: Irreversibility occurs when minima of $F$ are destroyed with changing $H$ or $T$.