Numerical Simulations and Replica Symmetry Breaking

TL;DR

This paper discusses large-scale numerical simulations of spin glasses, providing evidence for replica symmetry breaking in three dimensions without a magnetic field, and exploring the effects of magnetic fields on phase transitions.

Contribution

It demonstrates the use of advanced computer simulations to analyze spin glass phases and investigates the critical dimensions for phase transitions with and without magnetic fields.

Findings

RSB phase confirmed in 3D without magnetic field

Lower critical dimension for de Almeida-Thouless transition exceeds 3 with magnetic field

Large samples enable detailed comparison with laboratory experiments

Abstract

Use of dedicated computers in spin glass simulations allows one to equilibrate very large samples (of size as large as $L=32$) and to carry out "computer experiments" that can be compared to (and analyzed in combination with) laboratory experiments on spin-glass samples. In the absence of a magnetic field, the most economic conclusion of the combined analysis of equilibrium and non-equilibrium simulations is that an RSB spin glass phase is present in three spatial dimensions. However, in the presence of a field, the lower critical dimension for the de Almeida-Thouless transition seems to be larger than three.