The finite-size scaling (FSS) functions for anisotropic three-dimensional (3D) Ising models of size L 1 × L 1 × aL 1 ( a : anisotropy parameter) are studied by Monte Carlo simulations. We study the a dependence of FSS functions of the Binder parameter g and the magnetization distribution function p ( m ). We have shown that the FSS functions for p ( m ) at the critical temperature change from a two-peak structure to a single-peak one by increasing or decreasing a from 1. We also study the FSS near the critical temperature of the layered square-lattice Ising model, when the systems have a large two-dimensional (2D) anisotropy. We have found the 3D and 2D FSS behaviour depending on the parameter which is fixed; a unified view of 3D and 2D FSS behaviour has been obtained for the anisotropic 3D Ising models.The finite-size scaling (FSS) functions for anisotropic three-dimensional (3D) Ising models of size L 1 × L 1 × aL 1 ( a : anisotropy parameter) are studied by Monte Carlo simulations. We study the a dependence of FSS functions of the Binder parameter g and the magnetization distribution function p ( m ). We have shown that the FSS functions for p ( m ) at the critical temperature change from a two-peak structure to a single-peak one by increasing or decreasing a from 1. We also study the FSS near the critical temperature of the layered square-lattice Ising model, when the systems have a large two-dimensional (2D) anisotropy. We have found the 3D and 2D FSS behaviour depending on the parameter which is fixed; a unified view of 3D and 2D FSS behaviour has been obtained for the anisotropic 3D Ising models.

arXiv:cond-mat/9909262Journal of Physics A Mathematical and GeneralOct 13, 199914 citations

Finite-size scaling in the three-dimensional Ising model

Michael N. Barber, Robert B. Pearson, D. Toussaint +1 more

We have performed extensive studies of finite-size scaling in the three-dimensional Ising model, using a specially designed Ising processor. We show results for the susceptibility, the energy and specific heat, and the connected part of the fourth moment of the magnetization. Corrections to finite-size scaling are found to be small only for lattices of linear dimension greater than about L=24. This effect severely limits the accuracy to which critical parameters can be estimated. We estimate ${K}_{c}$ =0.221 650\ifmmode\pm\else\textpm\fi{}0.000 005 for the critical coupling, while exponent estimates are consistent with those obtained by other methods.We have performed extensive studies of finite-size scaling in the three-dimensional Ising model, using a specially designed Ising processor. We show results for the susceptibility, the energy and specific heat, and the connected part of the fourth moment of the magnetization. Corrections to finite-size scaling are found to be small only for lattices of linear dimension greater than about L=24. This effect severely limits the accuracy to which critical parameters can be estimated. We estimate ${K}_{c}$=0.221 650\ifmmode\pm\else\textpm\fi{}0.000 005 for the critical coupling, while exponent estimates are consistent with those obtained by other methods.

Physical review. B, Condensed matterAug 1, 1985134 citations

Finite-size calculations on the three-dimensional Ising model

Henk W. J. Blöte, G. Kamieniarz

Physica A Statistical Mechanics and its ApplicationsJun 1, 199322 citations

{K}_{c}

=0.221 650\ifmmode\pm\else\textpm\fi{}0.000 005 for the critical coupling, while exponent estimates are consistent with those obtained by other methods.