Monte Carlo Calculation of the Surface Free Energy for the 2d 7-state Potts Model, and an Estimate for 4d SU(3) Gauge Theory

TL;DR

This paper uses multicanonical Monte Carlo simulations to accurately compute the surface free energy of the 2d 7-state Potts model and provides a preliminary estimate for 4d SU(3) gauge theory surface tension.

Contribution

It introduces a multicanonical Monte Carlo method to precisely calculate surface free energy in the 2d Potts model and offers an initial estimate for 4d SU(3) gauge theory surface tension.

Findings

Surface tension of 2d 7-state Potts model is 0.0241 ± 0.0010.

The estimated surface tension for 4d SU(3) gauge theory is provided.

The results are significantly smaller than previous literature estimates.

Abstract

Using the recently proposed multicanonical ensemble, we perform Monte Carlo simulation for the 2d 7-state Potts model and calculate its surface free energy density (surface tension) to be $2 f^s = 0.0241 \pm 0.0010$. This is an order of magnitude smaller than other estimates in the recent literature. Relying on existing Monte Carlo data, we also give a preliminary estimate for the surface tension of 4d SU(3) lattice gauge theory with $L_t=2$.