Slow interaction dynamics in the spherical spin-glass model

Abstract

A surprising physical interpretation of the replica number n was unveiledin the study of the equilibrium properties of the coupledd ynamics of fast Ising spins andslow interactions: n is the ratio of the characteristic temperatures of the spin andthe interaction systems andcan take on any positive or negative real value, depending on the choice of the coupling dynamics. Here we investigate analytically the thermodynamics of the spherical spin-glass model for general n andd erive explicit equations for the transition lines separating the replica symmetric, replica symmetry broken andparamagnetic phases.