Real space rescaling study of spin glass behaviour in three dimensions

Abstract

The Edwards and Anderson model (1975) for spin glasses is investigated by a real space rescaling transformation on an S=¹/₂ Ising Hamiltonian with nearest-neighbour-only interactions in three dimensions. A transition to a spin glass ordered phase is found at about half the mean transition temperature, in contrast to earlier work on a two-dimensional model where no transition was found. The results suggest that the lower critical dimensionality, d_c, for spin glass order is slightly greater than 2, although possibly d_c=2 exactly. The specific heat is calculated and found to exhibit a broad maximum above T_c, with no discernable singularity at the transition since the exponent alpha is large and negative.