Slow interaction dynamics in spin-glass models

Abstract

The spin model of Coolen et al. (1993), involving slow dynamical laws for the couplings linking fast spins, is considered as a spin-glass model having explicit quenched disorder. The thermodynamic behaviour predicted is reminiscent of a Sherrington-Kirkpatrick spin-glass with one-step replica-symmetry breaking-generalizing the parallels of the simplest form of this model, which was entirely free of frozen disorder. However, even though the slow evolution of the couplings allows some balancing between achieving unfrustrated spin configurations and adopting those favoured by the quenched disorder, it is seen that this is not generally sufficient to avoid replica-symmetry breaking throughout the frozen phases. Moreover, there are seen to be two distinct types of spin-glass phase, each of which has both ergodic (replica-symmetric) and ergodicity-broken regimes.