Determination of the order of phase transitions in Potts model by the graph-weight approach

TL;DR

This paper introduces a graph-weight approach to determine the order of phase transitions in the Potts model, including non-integer states, by analyzing the probability distribution shape in various model cases.

Contribution

It presents a novel graph-based method for identifying phase transition order in the Potts model, applicable to non-integer states and different interaction ranges.

Findings

The method successfully distinguishes transition orders in 1D long-range Potts models.

It extends analysis to the mean-field limit of the Potts model.

The approach provides a new tool for studying phase transitions in complex systems.

Abstract

We examine the order of the phase transition in the Potts model by using the graph representation for the partition function, which allows treating a non-integer number of Potts states. The order of transition is determined by the analysis of the shape of the graph-weight probability distribution. The approach is illustrated on special cases of the one-dimensional Potts model with long-range interactions and on its mean-field limit.