Heisenberg Spin Glass on a Hypercubic Cell

TL;DR

This paper uses Monte Carlo simulations to study the phase transition and properties of an Heisenberg Spin Glass model on hypercubic lattices of varying dimensions, revealing a spin glass phase at low temperatures.

Contribution

It provides new simulation evidence for the existence of a spin glass phase in high-dimensional Heisenberg models and compares results with mean field and Bethe-Peierls predictions.

Findings

Evidence of a spin glass phase at low temperatures for D=8, 9, 10.

Inverse spin glass susceptibility grows linearly with T^2 at high temperatures.

Estimated critical temperatures agree with Bethe-Peierls approximation.

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}.