The spin glass transition of the three dimensional Heisenberg spin glass

TL;DR

This study uses advanced Monte Carlo simulations and finite size scaling to demonstrate a finite-temperature phase transition in three-dimensional Heisenberg spin glasses, revealing simultaneous spin and chiral glass orderings.

Contribution

It introduces a novel Monte Carlo algorithm adapted from lattice gauge theory, enabling larger system sizes and more accurate analysis of the phase transition in 3D Heisenberg spin glasses.

Findings

Finite-temperature phase transition confirmed

Both spin and chiral glass orderings develop at the same critical temperature

Large system sizes improve understanding of scaling corrections

Abstract

It is shown, by means of Monte Carlo simulation and Finite Size Scaling analysis, that the Heisenberg spin glass undergoes a finite-temperature phase transition in three dimensions. There is a single critical temperature, at which both a spin glass and a chiral glass orderings develop. The Monte Carlo algorithm, adapted from lattice gauge theory simulations, makes possible to thermalize lattices of size L=32, larger than in any previous spin glass simulation in three dimensions. High accuracy is reached thanks to the use of the Marenostrum supercomputer. The large range of system sizes studied allow us to consider scaling corrections.