Monte Carlo studies of critical free energies and the simple-cubic Ising model

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Abstract
This paper addresses the limitation for routine applications of the proposed Monte Carlo method of direct calculation of absolute free energy by sampling of finite-size dependences and discusses new extensions. The need for multistage sampling is removed and the method is now simpler to apply in practice. To exhibit this, the critical free-energy density for the simple-cubic nearest-neighbor ferromagnetic Ising model is studied for a wide range of lattice sizes, up to 32×32×32. The finite-size scaling is demonstrated and the scaling amplitude calculated with higher accuracy than before. These results indicate the possibility that very accurate free-energy density and related quantities such as surface free energy, can be routinely obtained for lattice models from Monte Carlo simulations, even at criticality.