New technique for replica symmetry breaking with application to the SK-model at and near T=0

TL;DR

This paper introduces a new method for analyzing high orders of replica-symmetry-breaking in the SK-model at low temperatures and zero temperature, providing a comprehensive framework for calculating observables and examining the transition to continuous RSB.

Contribution

The paper presents a novel direct approach to high-order RSB at low temperatures and zero temperature, avoiding approximations and scaling assumptions, and introduces a new continuous RSB formulation.

Findings

Able to treat high orders of RSB at T=0 directly

Provides the full range of the order function q(a,T)

Analyzes the approach to continuous RSB and proposes a new formulation

Abstract

We describe a novel method which allows the treatment of high orders of replica-symmetry-breaking (RSB) at low temperatures as well as at T=0 directly, without a need for approximations or scaling assumptions. It yields the low temperature order function q(a,T) in the full range $0\leq a <\infty$ and is complete in the sense that all observables can be calculated from it. The behavior of some observables and the finite RSB theory itself is analyzed as one approaches continuous RSB. The validity and applicability of the traditional continuous formulation is then scrutinized and a new continuous RSB formulation is proposed.