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 Tc(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, Jij. By extrapolation of Tc to zero, the lower borderline dimensionality is estimated as dl ≂2.5. High-temperature expansions for the spin-glass susceptibility of the ±J model in powers of w=tanh2(J/kBT) and u=tanh2(H/kBT), where H is the magnetic field, yield estimates of the magnetic field crossover exponent Δ for d=3 to 8.
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