Spin Models on Thin Graphs

TL;DR

This paper explores the use of analytical and numerical methods to study spin models, especially spin glasses, on thin random graphs, highlighting their similarities to Bethe lattice calculations and advantages for mean field analysis.

Contribution

It introduces a novel approach using thin graphs and methods from two-dimensional gravity to analyze spin models, bridging the gap between different graph-based techniques.

Findings

Thin graphs provide a useful framework for spin model analysis.

Methods from two-dimensional gravity can be applied to spin glasses.

Advantages over traditional Bethe lattice calculations are demonstrated.

Abstract

We discuss the utility of analytical and numerical investigation of spin models, in particular spin glasses, on ordinary ``thin'' random graphs (in effect Feynman diagrams) using methods borrowed from the ``fat'' graphs of two dimensional gravity. We highlight the similarity with Bethe lattice calculations and the advantages of the thin graph approach both analytically and numerically for investigating mean field results.