New method for studying the dynamics of disordered spin systems without finite-size effects

Abstract

A new method is presented that allows the determination of dynamical properties of disordered spin systems avoiding finite-size effects. The method is based on exact dynamical mean-field equations for the infinite large system. The resulting single-spin dynamics is solved by Monte Carlo simulations. We outline the formalism for the parallel dynamics of a fully connected model with random couplings. The decay of remanent magnetization of the model is studied. We find a power-law decay: m(t)-m(∞)∝${\mathit{t}}^{\mathrm{-}\mathit{a}}$, with a=0.474 and m(∞)=0.184 for the infinite system.