Free energy fluctuations in Ising spin glasses

TL;DR

This paper investigates the fluctuations of free energy in finite-dimensional Ising spin glasses, revealing limitations of the Parisi symmetry breaking scheme and proposing a modified approach for accurate results.

Contribution

It introduces a modified symmetry breaking scheme that correctly accounts for free energy fluctuations, improving upon the traditional Parisi scheme.

Findings

Parisi scheme fails for higher order free energy terms

Modified symmetry breaking scheme resolves the discrepancy

Provides more accurate predictions for spin glass fluctuations

Abstract

The sample-to-sample fluctuations of the free energy in finite-dimensional Ising spin glasses are calculated, using the replica method, from higher order terms in the replica number $n$. It is shown that the Parisi symmetry breaking scheme does not give the correct answers for these higher order terms. A modified symmetry breaking scheme with the same stability is shown to resolve the problem.