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

Kastening, Boris (2012):
Anisotropy and universality: Critical Binder cumulant of the two-dimensional Ising model.
In: Condensed Matter > Statistical Mechanics, arXiv.org, [Online-Edition: http://arxiv.org/pdf/1209.0105v1.pdf],
[Article]

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.

Item Type: Article
Erschienen: 2012
Creators: Kastening, Boris
Title: Anisotropy and universality: Critical Binder cumulant of the two-dimensional Ising model
Language: English
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.

Journal or Publication Title: Condensed Matter > Statistical Mechanics
Publisher: arXiv.org
Uncontrolled Keywords: Anisotropy, universality, critical point, Ising model, Binder cumulant
Divisions: 11 Department of Materials and Earth Sciences > Material Science > Advanced Thin Film Technology
11 Department of Materials and Earth Sciences > Material Science
11 Department of Materials and Earth Sciences
Date Deposited: 09 Jan 2013 09:52
Official URL: http://arxiv.org/pdf/1209.0105v1.pdf
Identification Number: arXiv:1209.0105
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