In this short note we collect together known results on the use of random matrix theory (RMT) 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...

A reduction procedure to obtain ground states of spin glasses on sparse graphs is developed and tested on the hierarchical lattice associated with the Migdal-Kadanoff approximation for low-dimensional lattices. While more generally applicable, these rules here lead to a complete reduction of the...

This paper deals with the derivation of a formula developed empirically in a previous article. The equation allows the calculation of the average electrical conductivity of two-component random media over the whole range of fraction and a wide range of resistivity ratio of the components....