Ensemble renormalization group for disordered systems

TL;DR

This paper introduces an ensemble renormalization group method tailored for disordered systems like spin glasses, maintaining key physical properties through distribution mapping, and validates it against hierarchical models with results matching Monte Carlo simulations.

Contribution

The paper presents a novel ensemble renormalization group approach for disordered systems, preserving physical properties and validated on hierarchical models.

Findings

Results agree with Monte Carlo simulations

Method effectively handles strong quenched disorder

Applicable to spin glasses and diluted ferromagnets

Abstract

We propose and study a renormalization group transformation that can be used also for models with strong quenched disorder, like spin glasses. The method is based on a mapping between disorder distributions, chosen such as to keep some physical properties (e.g., the ratio of correlations averaged over the ensemble) invariant under the transformation. We validate this ensemble renormalization group by applying it to the hierarchical model (both the diluted ferromagnetic version and the spin glass version), finding results in agreement with Monte Carlo simulations.