Eur. Phys. J. B (2013) 86: 30
https://doi.org/10.1140/epjb/e2012-30705-x

Regular Article

Universality aspects of the 2d random-bond Ising and 3d Blume-Capel models

¹ Departamento de Física Teórica I, Universidad Complutense, 28040 Madrid, Spain
² Faculty of Physics, University of Vienna, Boltzmanngasse 5, 1090 Vienna, Austria
³ Institute for Theoretical Physics and Center for Computational Materials Science, Vienna University of Technology, Hauptstraße 8-10, 1040 Vienna, Austria

^a e-mail: nfytas@phys.uoa.gr

Received: 31 July 2012
Received in final form: 1 November 2012
Published online: 31 January 2013

Abstract

We report on large-scale Wang-Landau Monte Carlo simulations of the critical behavior of two spin models in two- (2d) and three-dimensions (3d), namely the 2d random-bond Ising model and the pure 3d Blume-Capel model at zero crystal-field coupling. The numerical data we obtain and the relevant finite-size scaling analysis provide clear answers regarding the universality aspects of both models. In particular, for the random-bond case of the 2d Ising model the theoretically predicted strong universality’s hypothesis is verified, whereas for the second-order regime of the Blume-Capel model, the expected d = 3 Ising universality is verified. Our study is facilitated by the combined use of the Wang-Landau algorithm and the critical energy subspace scheme, indicating that the proposed scheme is able to provide accurate results on the critical behavior of complex spin systems.