First order phase transition of the q-state Potts model in two dimensions

TL;DR

This paper uses large-$q$ series expansions to precisely analyze the first order phase transition in the 2D q-state Potts model, revealing detailed properties of energy cumulants, magnetization, correlation length, and the spectrum of excited states.

Contribution

It introduces a large-$q$ series method to accurately estimate physical quantities at the phase transition, surpassing Monte Carlo precision, and characterizes the excitation spectrum at the transition point.

Findings

Energy and magnetization cumulants are estimated with 10^2-10^4 times higher precision.

Excited states form a continuum spectrum with no particle state at the transition.

The transfer matrix eigenvalues support the continuum spectrum conclusion.

Abstract

We have calculated the large-$q$ series of the energy cumulants, the magnetization cumulants and the correlation length at the first order phase transition point both in the ordered and disordered phases for the $q$-state Potts model in two dimensions. The series enables us to estimate the numerical values of the quantities more precisely by a factor of $10^2 - 10^4$ than the Monte Carlo simulations. From the large-$q$ series of the eigenvalues of the transfer matrix, we also find that the excited states form a continuum spectrum and there is no particle state at the first order phase transition point.