Monte Carlo computation of cluster free energies in the Ising model: a test for the validity of the capillarity approximation

Abstract

A new Monte Carlo technique is proposed to compute directly the free energy difference F_N+1-F_N of two clusters with size N+1 and N. The algorithm is applied to the two-dimensional square Ising model with nearest-neighbour interactions. Results are given for 1N is confirmed by the values of the internal energy U_N obtained as a by-product of the calculation.