The ordered phase of the one-dimensional Ising spin glass with long-range interactions

TL;DR

This paper re-examines the renormalization group equations for the one-dimensional long-range Ising spin glass, revealing a new fixed point and supporting the replica symmetric phase within certain interaction ranges.

Contribution

It identifies a new fixed point in the RG equations and clarifies the nature of the spin glass phase, aligning with droplet model predictions.

Findings

Discovery of a new fixed point in RG analysis.

Confirmation that the spin glass phase is replica symmetric.

Agreement with droplet model expectations.

Abstract

The one-dimensional long-range Ising spin glass provides useful insights into the properties of finite dimensional spin glasses with short-range interactions. The defect energy renormalization group equations derived for it by Kotliar, Anderson and Stein have been re-examined and a new fixed point has been found. The fixed points which have previously been studied are found to be inappropriate. It is shown that the renormalization group equations themselves directly imply that the spin glass phase is replica symmetric, in agreement with droplet model expectations, when the range exponent $\sigma$ lies between the upper and lower critical values.