Monte Carlo studies of the critical free energies for the three-dimensional Ising model with surfaces, edges, and corners

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Abstract
We present an extensive Monte Carlo study of the three-dimensional Ising model with free surfaces, edges, and corners at bulk criticality. Finite-size scaling properties of the excess free energies of free surfaces, edges, and corners are estimated by use of the recently proposed applications of the parametric integration method. The corner excess free energies are obtained for the first time and are consistent with the logarithmic finite-size scaling predictions. Results of the simplecubic and body-centered-cubic lattices provide support for the proposed universality of the finite-size scaling amplitudes for the excess free energies of free surfaces, edges, and corners.