Cavity Approach to the Random Solid State

TL;DR

This paper applies the cavity approach to analyze the physical properties of random solids, focusing on particle localization and localization length distribution, providing insights into their thermal motion and confirming previous theoretical results.

Contribution

It introduces the cavity approach as a new method to study random solids, offering a different perspective from replica mean-field theory.

Findings

Confirms previous results on localization fractions and lengths

Provides a physical interpretation of the properties of random solids

Applicable to rubbery media and chemical gels

Abstract

The cavity approach is used to address the physical properties of random solids in equilibrium. Particular attention is paid to the fraction of localized particles and the distribution of localization lengths characterizing their thermal motion. This approach is of relevance to a wide class of random solids, including rubbery media (formed via the vulcanization of polymer fluids) and chemical gels (formed by the random covalent bonding of fluids of atoms or small molecules). The cavity approach confirms results that have been obtained previously via replica mean-field theory, doing so in a way that sheds new light on their physical origin.