Potts model on complex networks

TL;DR

This paper investigates how the nature of phase transitions in the Potts model changes on complex networks with fat-tailed degree distributions, revealing a shift from first-order to continuous transitions and providing exact solutions for specific cases.

Contribution

It demonstrates the suppression of first-order phase transitions in the Potts model on fat-tailed networks and derives exact solutions for the p=1 case, linking it to percolation theory.

Findings

First-order transition is suppressed on fat-tailed networks.

Transition becomes continuous and of infinite order.

Exact solution for p=1 case matches percolation results.

Abstract

We consider the general p-state Potts model on random networks with a given degree distribution (random Bethe lattices). We find the effect of the suppression of a first order phase transition in this model when the degree distribution of the network is fat-tailed, that is, in more precise terms, when the second moment of the distribution diverges. In this situation the transition is continuous and of infinite order, and size effect is anomalously strong. In particular, in the case of $p=1$, we arrive at the exact solution, which coincides with the known solution of the percolation problem on these networks.