The Ising spin glass in finite dimensions: a perturbative study of the free energy

TL;DR

This paper uses replica field theory to analyze the free energy of the Ising spin glass in finite dimensions, revealing Gaussian deviations and exploring the replica symmetry breaking transition near the Almeida-Thouless line.

Contribution

It provides a perturbative analysis of the free energy in finite-dimensional Ising spin glasses, connecting the replica symmetry breaking transition to the Almeida-Thouless line.

Findings

Free energy deviations are Gaussian regardless of order parameter structure.

The zero line n(T) matches the Almeida-Thouless line for d>8.

The behavior in 6<d<8 dimensions is complex with multiple possible scenarios.

Abstract

Replica field theory is used to study the n-dependent free energy of the Ising spin glass in a first order perturbative treatment. Large sample-to-sample deviations of the free energy from its quenched average prove to be Gaussian, independently of the special structure of the order parameter. The free energy difference between the replica symmetric and (infinite level) replica symmetry broken phases is studied in details: the line n(T) where it is zero coincides with the Almeida-Thouless line for d>8. The dimensional domain 6<d<8 is more complicated, and several scenarios are possible.