Kastening, Boris (2012)
Anisotropy and universality: Critical Binder cumulant of the two-dimensional Ising model.
In: Condensed Matter > Statistical Mechanics
Artikel, Bibliographie
Kurzbeschreibung (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.
| Typ des Eintrags: | Artikel |
|---|---|
| Erschienen: | 2012 |
| Autor(en): | Kastening, Boris |
| Art des Eintrags: | Bibliographie |
| Titel: | Anisotropy and universality: Critical Binder cumulant of the two-dimensional Ising model |
| Sprache: | Englisch |
| Publikationsjahr: | 4 September 2012 |
| Verlag: | arXiv.org |
| Titel der Zeitschrift, Zeitung oder Schriftenreihe: | Condensed Matter > Statistical Mechanics |
| URL / URN: | http://arxiv.org/pdf/1209.0105v1.pdf |
| Kurzbeschreibung (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. |
| Freie Schlagworte: | Anisotropy, universality, critical point, Ising model, Binder cumulant |
| ID-Nummer: | arXiv:1209.0105 |
| Fachbereich(e)/-gebiet(e): | 11 Fachbereich Material- und Geowissenschaften > Materialwissenschaft > Fachgebiet Dünne Schichten 11 Fachbereich Material- und Geowissenschaften > Materialwissenschaft 11 Fachbereich Material- und Geowissenschaften |
| Hinterlegungsdatum: | 09 Jan 2013 09:52 |
| Letzte Änderung: | 05 Mär 2013 10:04 |
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