Dynamical mean-field theory for spin glasses. II. Approach to equilibrium in a small field

Abstract

For pt.I see ibid., vol.16, no.7, p.1219 (1983). The response of a simple infinite-range model of a spin glass to the imposition of a small external field is studied. The field is turned on at t=0, and the evolution of the spin correlations is followed as processes involving flips of successively larger and larger clusters of spins occur, until equilibrium is achieved at t= infinity . The evolution from one state to the other proceeds through a quasi-continuum of intermediate metastable states labelled by the fraction y of spins that flip simultaneously on that time scale. The time scale for such processes grows very long as the size N of the system increases (possibly like exp((Ny)¹2/T_g/T)), so in the infinite system, only an infinitesimal fraction of this evolution can be observed. The generalised equation of state describing the evolution of correlations has the form derived by Sompolinsky, but the physical interpretation is different. In particular, the author does not postulate any violation of the fluctuation-dissipation theorem in equilibrium; the terms in the equations which correspond to those which violate it in his theory have the form they do because a non-equilibrium situation is being described. The physical interpretation of the variable y also allows an additional relation between initial- and final-state correlation functions which leads to the Parisi equation for his order parameter q(x), with x=1-y.