Low-concentration series expansions for dilute spin glasses at zero temperature

An Ising (spin-¹/₂) model with random positive, negative and zero nearest-neighbour exchange coefficients is considered at zero temperature. The authors define two 'spin glass' susceptibilities, through average sums over ((s_is_j)²)_av and ( mod (s_is_j) mod )_av, where ( ) means averaging over degenerate ground states and ( )_av means averaging over the random bond distribution. These susceptibilities are expanded in powers of the concentrations of the non-zero bonds, for the triangular (seven terms), square (nine terms) and d-dimensional hypercubic (eight terms) lattices. All the series show a singularity, which is associated with the paramagnetic to spin-glass phase transition. The phase boundary between these phases, and the corresponding critical exponents, are estimated.