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Physical Review Letters

Direct Calculation of Absolute Free Energy for Lattice Systems by Monte Carlo Sampling of Finite-Size Dependence

K. K. Mon

Published Jun 24, 1985• 43 citations
Publisher

Abstract

It is shown that the absolute free energy of lattice spin systems can be calculated directly by a novel application of Monte Carlo sampling of finite-size dependence. Results are obtained for the two- and three-dimensional Ising models at ${T}_{c}$ and are consistent with recent finite-size scaling-theory predictions. The free energy is in excellent agreement with Onsager's exact solution for two dimensions and with series expansions for three dimensions. The ${U}_{0}$ is measured for the first time. Results are consistent with the proposed universality.

DOI
10.1103/physrevlett.54.2671

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It is shown that the absolute free energy of lattice spin systems can be calculated directly by a novel application of Monte Carlo sampling of finite-size dependence. Results are obtained for the two- and three-dimensional Ising models at Tc{T}_{c}Tc​ and are consistent with recent finite-size scaling-theory predictions. The free energy is in excellent agreement with Onsager's exact solution for two dimensions and with series expansions for three dimensions. The U0{U}_{0}U0​ is measured for the first time. Results are consistent with the proposed universality.
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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.
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