LOW-TEMPERATURE PHASE OF THE ISING SPIN-GLASS ON A HYPERCUBIC LATTICE

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 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/d2, and find an enhancement of replica-symmetry-breaking effects as the dimension is decreased. © 1990 The American Physical Society.