Replica Real Space Renormalization Group for Spin Glasses

TL;DR

This paper develops a real space renormalization group method for Ising spin glasses using replicas, exploring replica symmetry breaking to incorporate non-linear effects within the RG framework.

Contribution

It introduces a replica-based RG approach for spin glasses and discusses the integration of replica symmetry breaking into the RG scheme.

Findings

Replica symmetric RG results align with simple decimation.

Inclusion of replica symmetry breaking introduces non-linear RG effects.

The method provides a framework for analyzing spin glasses beyond simple approximations.

Abstract

We construct a real space renormalization group (RG) approach for Ising spin glasses on hypercubic lattices within the scheme of the Migdal-Kadanoff approximation using replicas. Our replica symmetric solution yields results consistent with simple decimation previously obtained and the introduction of breaking of replica symmetry within the RG is discussed, which inserts in a natural fashion non-linear RG into the problem.