Short-range Ising spin glasses in general dimensions

Abstract

The equilibrium properties of nearest‐neighbor Ising spin glasses on hypercubic lattices are studied as a function of d, the dimensionality. An expansion of T_c(d) to fifth order in inverse powers of d, augmented by high‐temperature series estimates for d=3 and 4, yields the critical temperature for all d and for general, symmetric distributions of coupling strengths, J_ij. By extrapolation of T_c to zero, the lower borderline dimensionality is estimated as d_l ≂2.5. High‐temperature expansions for the spin‐glass susceptibility of the ±J model in powers of w=tanh²(J/k_BT) and u=tanh²(H/k_BT), where H is the magnetic field, yield estimates of the magnetic field crossover exponent Δ for d=3 to 8.