Large-scale Monte Carlo simulations of the isotropic three-dimensional Heisenberg spin glass

TL;DR

This study uses large-scale Monte Carlo simulations to investigate the three-dimensional Heisenberg spin glass, revealing that its critical behavior is consistent with a lower critical dimension near three, with spins and chiralities showing similar behavior.

Contribution

It provides new large-scale simulation data suggesting the lower critical dimension of the Heisenberg spin glass is close to three, with detailed analysis of spin and chirality behavior.

Findings

Data indicates marginal behavior at larger sizes

Lower critical dimension likely close to three

Spins and chiralities behave similarly

Abstract

We study the Heisenberg spin glass by large-scale Monte Carlo simulations for sizes up to 32^3, down to temperatures below the transition temperature claimed in earlier work. The data for the larger sizes show more marginal behavior than that for the smaller sizes, indicating the lower critical dimension is close to, and possibly equal to three. We find that the spins and chiralities behave in a quite similar manner.