Heisenberg spin glass on a hypercubic cell

We present results of a Monte Carlo simulation of a Heisenberg spin glass model on a hypercubic 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→∞. 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 T2 as in the mean field case. Estimates of Tc 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.