Large Energy Cumulants in the 2D Potts Model and their Effects in Finite Size Analysis

TL;DR

This paper introduces an ansatz for the free energy of the 2D q-states Potts model near its first order transition, revealing large energy cumulants that significantly impact finite size analysis for moderate q values.

Contribution

It proposes a new ansatz for the free energy and highlights how large energy cumulants influence finite size scaling in the Potts model.

Findings

Energy profile at transition not Gaussian for q ≤ 15

Finite size corrections governed by a length scale much larger than correlation length

Large energy cumulants affect traditional finite size analysis

Abstract

We develop an ansatz for expressing the free energy of the two dimensional $q$-states Potts model for $q > 4$ near its first order phase transition point. We notice that for the moderate values of $ q \lesssim 15 $, the energy profile at the phase transition is not expressible as a sum of gaussians. We discuss how this affects the traditional finite size analysis of this phase transition. In particular, the dominant length scale governing the finite size corrections turns out to be much (${} \sim 6$ ~times) larger than the largest correlation length in the problem.