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

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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.

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Authors and Affiliations

  1. Departamento de Física Teórica I, Universidad Complutense, 28040, Madrid, Spain

    Nikolaos G. Fytas

  2. Faculty of Physics, University of Vienna, Boltzmanngasse 5, 1090, Vienna, Austria

    Panagiotis E. Theodorakis

  3. Institute for Theoretical Physics and Center for Computational Materials Science, Vienna University of Technology, Hauptstraße 8-10, 1040, Vienna, Austria

    Panagiotis E. Theodorakis

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  1. Nikolaos G. Fytas
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Correspondence to Nikolaos G. Fytas.

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Fytas, N.G., Theodorakis, P.E. Universality aspects of the 2d random-bond Ising and 3d Blume-Capel models. Eur. Phys. J. B 86, 30 (2013). https://doi.org/10.1140/epjb/e2012-30705-x

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