Phase Transitions in the 1-d Long-Range Diluted Heisenberg Spin Glass

TL;DR

This study uses Monte Carlo simulations to explore phase transitions in a one-dimensional long-range diluted Heisenberg spin glass, revealing different behaviors in mean-field and non-mean-field regimes related to the interaction decay parameter.

Contribution

It demonstrates how varying the decay parameter sigma in a 1D long-range model can emulate different effective dimensions, providing insights into phase transition behaviors in spin glasses.

Findings

Evidence of chiral glass transition temperature exceeding spin glass temperature at certain sigma.

No such evidence found for other sigma values.

The model captures both mean-field and non-mean-field regimes.

Abstract

We use Monte Carlo simulations to study the one-dimensional long-range diluted Heisenberg spin glass with interactions that fall as a power, sigma, of the distance. Varying the power is argued to be equivalent to varying the space dimension of a short-range model. We are therefore able to study both the mean-field and non-mean-field regimes. For one value of sigma, in the non-mean-field regime, we find evidence that the chiral glass transition temperature may be somewhat higher than the spin glass transition temperature. For the other values of sigma we see no evidence for this.