Low-temperature phase of the Ising spin glass on a hypercubic lattice

Abstract

We consider the free energy, averaged over disorder using the replica method, of an Ising spin glass on a d-dimensional hypercubic lattice. We demonstrate that the free energy can be expanded in powers of 1/d, and that the zeroth-order (d=∞) result recovers thermodynamics identical to that of the Sherrington-Kirpatrick model. We explicitly solve the model near (and below) its spin-glass critical temperature to order 1/${\mathit{d}}^2$, and find an enhancement of replica-symmetry-breaking effects as the dimension is decreased.