Numerical test of the replica-symmetric Hamiltonian for the correlations of the critical state of spin glasses in a field

TL;DR

This paper tests the validity of the Bray and Roberts replica-symmetric Hamiltonian in describing correlations in the critical state of spin glasses in a magnetic field, using numerical simulations in four dimensions and on the Bethe lattice.

Contribution

It provides numerical confirmation that the Bray and Roberts field theory accurately models the correlations of the critical spin glass state.

Findings

Confirmation of Bray and Roberts theory in 4D spin glasses

Validation of the theory on the Bethe lattice

Support for the effective field theory of glassy correlations

Abstract

A growing body of evidence indicates that the sluggish low-temperature dynamics of glass formers (e.g. supercooled liquids, colloids or spin glasses) is due to a growing correlation length. Which is the effective field theory that describes these correlations? The natural field theory was drastically simplified by Bray and Roberts in 1980. More than forty years later, we confirm the tenets of Bray and Roberts theory by studying the Ising spin glass in an externally applied magnetic field, both in four spatial dimensions (data obtained from the Janus collaboration) and on the Bethe lattice.