Statistical description of domains in the Potts model

TL;DR

This paper analyzes the statistical distributions of domain sizes in the Potts model near phase transitions, revealing power law behavior at criticality and suppression beyond it, linking inhomogeneity with Zipf's law.

Contribution

It provides a detailed statistical description of domain mass distributions in the Potts model, highlighting the transition from power law to suppressed tails near critical points.

Findings

Power law distribution at critical temperature

Suppressed power law tail beyond critical point

Connection between inhomogeneity and Zipf's law

Abstract

The Zipf power law and its connection with the inhomogeneity of the system is investigated. We describe the statistical distributions of the domain masses in the Potts model near the temperature-induced phase transition. We found that the statistical distribution near the critical point is described by the power law form with a long tail, while beyond the critical point the power law tail is suppressed.