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arXiv · 1209.0105

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

Boris Kastening
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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.

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Boris Kastening. 2013-04-24. Anisotropy and universality: Critical Binder cumulant of the two-dimensional Ising model. https://doi.org/10.1103/physreve.87.044101

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