Vanishing of the Edwards-Anderson order parameter in two- and three-dimensional Ising spin glasses

Abstract

The nature of the freezing process in two- and three-dimensional Ising spin glasses with bonds J_ij=+or-J has been investigated. Monte Carlo simulations indicate that the characteristic cusp in the susceptibility chi is a non-equilibrium phenomenon resulting from the finite observation times available for the computation of chi (or its experimental measurement). This picture of the freezing process, which is illustrated by explicit calculation for the one-dimensional Ising spin glass, implies chi =1/k_BT for all temperatures, or that the Edwards-Anderson order parameter q vanishes. Investigation of the ground states of certain periodic models in two and three dimensions show that every spin belongs to a finite cluster which may be turned over with no cost of energy, so that q is rigorously zero for such models. It is argued that this result holds also for the fully random models.