Random Matrix Theory in Lattice Statistical Mechanics
J.-Ch. Angles d'Auriac, J.-M. Maillard
TL;DR
This paper reviews how Random Matrix Theory (RMT) is used in lattice statistical mechanics to characterize integrability and discover new integrable models, with examples from quantum and classical systems.
Contribution
It compiles known RMT results and highlights its dual role in characterizing integrability and aiding in the discovery of new integrable models.
Findings
RMT characterizes integrability in lattice models
RMT helps identify new integrable models
Examples from quantum and classical systems illustrate these points
Abstract
In this short note we collect together known results on the use of Random Matrix Theory in lattice statistical mechanics. The purpose here is two fold. Firstly the RMT analysis provides an intrinsic characterization of integrability, and secondly it appears to be an effective tool to find new integrable models. Various examples from quantum and classical statistical mechanics are presented.
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Taxonomy
TopicsRandom Matrices and Applications · Theoretical and Computational Physics · Stochastic processes and statistical mechanics