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

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 $L_t=2$.