Infinite Volume Relaxation in the Sherrington-Kirkpatrick Model

Abstract

In a recent work (Eissfeller and Opper, 1992) a numerical method has been proposed to simulate off-equilibrium zero-temperature parallel dynamics for the SK model without finite size effects. We study the extension of the method to non-zero temperature and sequential dynamics, and analyze more carefully the involved computational problems. We find evidence, in the glassy phase, for an algebraic relaxation of the energy density to its equilibrium value, at least at large enough temperatures, and for an algebraic relaxation of the magnetization to zero at non-zero temperatures, with an exponent directly proportional to the temperature.