Scaling and Renormalization Group in Replica Symmetry Breaking space: Evidence for a simple analytical solution of the SK model at zero temperature

TL;DR

This paper provides evidence for a simple analytical solution of the SK spin glass model at zero temperature by combining numerical RSB solutions with renormalization group analysis, revealing a fixed point order function.

Contribution

It introduces a conjectured fixed point order function q*(a) for the SK model at zero temperature, derived from RSB and renormalization group methods, suggesting a new analytical approach.

Findings

Evidence for a non-trivial T->0 limit of q(x)

Proposal of a fixed point order function q*(a)

Identification of a correlation length  in RSB-space

Abstract

Using numerical self-consistent solutions of a sequence of finite replica symmetry breakings (RSB) and Wilson's renormalization group but with the number of RSB-steps playing a role of decimation scales, we report evidence for a non-trivial T->0-limit of the Parisi order function q(x) for the SK spin glass. Supported by scaling in RSB-space, the fixed point order function is conjectured to be q*(a)=sqrt{\pi/2} a/\xi erf(\xi/a) on 0\leq a\leq infty where x/T->a at T=0 and \xi\approx 1.13\pm 0.01. \xi plays the role of a correlation length in a-space. q*(a) may be viewed as the solution of an effective 1D field theory.