Random elastic networks : strong disorder renormalization approach

TL;DR

This paper introduces a strong disorder real-space renormalization method for arbitrary networks of random masses and springs, extending previous approaches and analyzing its accuracy through comparison with exact rules.

Contribution

It generalizes existing RG procedures for disordered elastic networks and provides a framework for understanding their accuracy and applicability.

Findings

The RG approach effectively simplifies complex disordered networks.

Comparison with Aoki RG rules confirms the accuracy of the method.

The method is applicable to a wide class of disordered elastic systems.

Abstract

For arbitrary networks of random masses connected by random springs, we define a general strong disorder real-space renormalization (RG) approach that generalizes the procedures introduced previously by Hastings [Phys. Rev. Lett. 90, 148702 (2003)] and by Amir, Oreg and Imry [Phys. Rev. Lett. 105, 070601 (2010)] respectively. The principle is to eliminate iteratively the elementary oscillating mode of highest frequency associated with either a mass or a spring constant. To explain the accuracy of the strong disorder RG rules, we compare with the Aoki RG rules that are exact at fixed frequency.