Heisenberg Spin Glass on a Hypercubic Cell

We present results of a Monte Carlo simulation of an Heisenberg Spin Glass model on a hipercubic cell of size 2 in D dimensions. Each spin interacts with D nearest neighbors and the lattice is expected to recover the completely connected (mean field) limit as D !1. An analysis of the Binder parameter for D = 8; 9 and 10 shows clear evidence of the presence of a spin glass phase at low temperatures. We found that in the high temperature regime the inverse spin glass susceptibility grows linearly with T 2 as in the mean field case. Estimates of T c from the high temperature data are in very good agreement with the results of a Bethe-Peierls approximation for an Heisenberg Spin Glass with coordination number D. 1 Introduction Despite the fact that many real spin glasses, like Eu x Sr 1\Gammax S; CuMn;AgMn , are Heisenberg like systems, the very existence of a finite temperature transition in three dimensions seems to be ruled out for systems with short range interactions [1]. Simulat..