Tunneling and the Spectrum of the Potts Model

TL;DR

This paper investigates the spectrum of the three-dimensional three-state Potts model near its phase transition using high-statistics simulations, revealing spectral classifications, phase interface behaviors, and a new method for measuring surface tension.

Contribution

It introduces a spectral analysis approach for the Potts model spectrum near phase transitions and a novel method to determine surface tension.

Findings

Spectrum near phase transition matches a four-component Hamiltonian model

Ordered interfaces often involve an intermediate disordered phase

New spectral method effectively measures surface tension

Abstract

The three-dimensional, three-state Potts model is studied as a paradigm for high temperature quantum chromodynamics. In a high statistics numerical simulation using a Swendson-Wang algorithm, we study cubic lattices of dimension as large as $64^3$ and measure correlation functions on long lattices of dimension $20^2\times 120$ and $30^2\times 120$. These correlations are controlled by the spectrum of the transfer matrix. This spectrum is studied in the vicinity of the phase transition. The analysis classifies the spectral levels according to an underlying $S_3$ symmetry. Near the phase transition the spectrum agrees nicely with a simple four-component hamiltonian model. In the context of this model, we find that low temperature ordered-ordered interfaces nearly always involve a disordered phase intermediate. We present a new spectral method for determining the surface tension between phases.