Anisotropy and universality: Critical Binder cumulant of the two-dimensional Ising model

Abstract

We reanalyze transfer matrix and Monte Carlo results for the critical Binder cumulant U* of an anisotropic two-dimensional Ising model on a square lattice in a square geometry with periodic boundary conditions. Spins are coupled between nearest neighboring sites and between next-nearest neighboring sites along one of the lattice diagonals. We find that U* depends only on the asymptotic critical long-distance features of the anisotropy, irrespective of its realization through ferromagnetic or antiferromagnetic next-nearest neighbor couplings. We modify an earlier renormalization-group calculation to obtain a quantitative description of the anisotropy dependence of U*. Our results support our recent claim towards the validity of universality for critical phenomena in the presence of a weak anisotropy.

4 pages, 2 figures; one reference and some clarifications added

References in corpus (5)

• Critical Binder cumulant in two-dimensional anisotropic Ising models
• Critical Binder cumulant for isotropic Ising models on square and triangular lattices
• Diversity of critical behavior within a universality class
• Dynamic critical behavior of model A in films: Zero-mode boundary conditions and expansion near four dimensions
• Universal anisotropic finite-size critical behavior of the two-dimensional Ising model on a strip and of d-dimensional models on films

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• Multiparameter universality and conformal field theory for anisotropic confined systems: test by Monte Carlo simulations
• Continuous demixing transition of binary liquids: finite-size scaling from the analysis of sub-systems