Replica symmetric spin glass field theory

TL;DR

This paper introduces a new method using the replicon generator function g(v) to analyze the stability of the replica symmetric spin glass phase, revealing instability below six dimensions and discussing potential breakdown of mean field theory at low dimensions.

Contribution

It proposes a novel stability testing method for the replica symmetric phase using the replicon generator function g(v), with exact and perturbative analyses.

Findings

Replica symmetric phase is unstable for dimensions d<6.

The mean field scaling function is highly robust.

Infrared divergence may cause mean field breakdown at low dimensions.

Abstract

A new powerful method to test the stability of the replica symmetric spin glass phase is proposed by introducing a replicon generator function g(v). Exact symmetry arguments are used to prove that its extremum is proportional to the inverse spin glass susceptibility. By the idea of independent droplet excitations a scaling form for g(v) can be derived, whereas it can be exactly computed in the mean field Sherrington-Kirkpatrick model. It is shown by a first order perturbative treatment that the replica symmetric phase is unstable down to dimensions d<6, and the mean field scaling function proves to be very robust. Although replica symmetry breaking is escalating for decreasing dimensionality, a mechanism caused by the infrared divergent replicon propagator may destroy the mean field picture at some low enough dimension.