Universal finite-size scaling analysis of Ising models with long-range interactions at the upper critical dimensionality: Isotropic case

Daniel Grüneberg and Alfred Hucht
Phys. Rev. E 69, 036104 – Published 9 March 2004
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Abstract

We investigate a two-dimensional Ising model with long-range interactions that emerge from a generalization of the magnetic dipolar interaction in spin systems with in-plane spin orientation. This interaction is, in general, anisotropic whereby in the present work we focus on the isotropic case for which the model is found to be at its upper critical dimensionality. To investigate the critical behavior the temperature and field dependence of several quantities are studied by means of Monte Carlo simulations. On the basis of the Privman-Fisher hypothesis and results of the renormalization group the numerical data are analyzed in the framework of a finite-size scaling analysis and compared to finite-size scaling functions derived from a Ginzburg-Landau-Wilson model in zero mode (mean-field) approximation. The obtained excellent agreement suggests that at least in the present case the concept of universal finite-size scaling functions can be extended to the upper critical dimensionality.

  • Received 10 October 2003

DOI:https://doi.org/10.1103/PhysRevE.69.036104

©2004 American Physical Society

Authors & Affiliations

Daniel Grüneberg* and Alfred Hucht

  • Fakultät für Naturwissenschaften, Theoretische Physik, Universität Duisburg-Essen, D-47048 Duisburg, Germany

  • *Electronic address: daniel@thp.Uni-Duisburg.de
  • Electronic address: fred@thp.Uni-Duisburg.de

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Vol. 69, Iss. 3 — March 2004

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