Potts Model On Random Trees

TL;DR

This paper investigates the Potts model on random graphs with tree-like structures, employing numerical methods and simulations to analyze its behavior and compare with previous assumptions about local fields.

Contribution

It introduces a population dynamics algorithm for exact numerical solutions of the Potts model on complex networks and highlights limitations of earlier uniform field assumptions.

Findings

Population dynamics provides accurate solutions.

Uniform local field assumption fails for low-degree nodes.

Results validated through simulations.

Abstract

We study the Potts model on locally tree-like random graphs of arbitrary degree distribution. Using a population dynamics algorithm we numerically solve the problem exactly. We confirm our results with simulations. Comparisons with a previous approach are made, showing where its assumption of uniform local fields breaks down for networks with nodes of low degree.