arXiv:1209.0105 · Physical Review E

Anisotropy and universality in finite-size scaling: Critical Binder cumulant of a two-dimensional Ising model

Boris Kastening

Published Apr 19, 2013• 9 citations

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 universal finite-size scaling for critical phenomena in the presence of a weak anisotropy.

DOI: 10.1103/physreve.87.044101

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