In our recent letter [1], we address the disagreement between renormalization group (RG) analytical prediction [2] and Monte Carlo simulation [3] for the magnetization distribution cumulants of the five-dimensional Ising model. The Monte Carlo data [3] for finite lattices ( L ⩽ 17) did not agree with the RG predictions for the large- L limit [2]. We explore the possibility that this difference can be traced to strong finite-size corrections. Therefore, we calculate numerically the RG predictions for the finite-size corrections [1]. Our numerical RG finite-size corrections can be described very well with a square-root dependence L [( − 1)/(2)] . Such a power law was predicted in the RG paper [2] to be the leading correction term. Then, we compare the numerical RG predictions for the finite-size correction to the deviations of the Monte Carlo data from the RG predictions for the large- L limit. We find good agreement for the first and third absolute moment. For the fourth-order Binder cumulant, only the Monte Carlo data for the larger lattices is in agreement with the numerical RG predictions.In our recent letter [1], we address the disagreement between renormalization group (RG) analytical prediction [2] and Monte Carlo simulation [3] for the magnetization distribution cumulants of the five-dimensional Ising model. The Monte Carlo data [3] for finite lattices ( L ⩽ 17) did not agree with the RG predictions for the large- L limit [2]. We explore the possibility that this difference can be traced to strong finite-size corrections. Therefore, we calculate numerically the RG predictions for the finite-size corrections [1]. Our numerical RG finite-size corrections can be described very well with a square-root dependence L [( − 1)/(2)] . Such a power law was predicted in the RG paper [2] to be the leading correction term. Then, we compare the numerical RG predictions for the finite-size correction to the deviations of the Monte Carlo data from the RG predictions for the large- L limit. We find good agreement for the first and third absolute moment. For the fourth-order Binder cumulant, only the Monte Carlo data for the larger lattices is in agreement with the numerical RG predictions.

Europhysics Letters (EPL)Mar 1, 19976 citations

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

K. K. Mon

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\ifmmode\times\else\texttimes\fi{}32\ifmmode\times\else\texttimes\fi{}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.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\ifmmode\times\else\texttimes\fi{}32\ifmmode\times\else\texttimes\fi{}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.

Physical review. B, Condensed matterJan 1, 198925 citations

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

K. K. Mon

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.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.

Physical Review LettersJun 24, 198543 citations

{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.