Heisenberg Spin Glass on a Hypercubic Cell

Abstract

We present results of a Monte Carlo simulation of an Heisenberg Spin Glass model on a hipercubic cell of size 2 in {\it D} dimensions. Each spin interacts with {\it D} nearest neighbors and the lattice is expected to recover the completely connected (mean field) limit as $D\rightarrow \infty$. 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 {\it D}.