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

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Abstract
A new Monte Carlo technique is proposed to compute directly the free energy difference FN+1-FN 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 UN obtained as a by-product of the calculation.