Classical critical behavior of spin models with long-range interactions

Erik Luijten, Henk W J Blöte

Research output: Contribution to journalArticle

163 Scopus citations


We present the results of extensive Monte Carlo simulations of Ising models with algebraically decaying ferromagnetic interactions in the regime where classical critical behavior is expected for these systems. We corroborate the values for the exponents predicted by renormalization theory for systems in one, two, and three dimensions and accurately observe the predicted logarithmic corrections at the upper critical dimension. We give both theoretical and numerical evidence that above the upper critical dimension the decay of the critical spin-spin correlation function in finite systems consists of two different regimes. For one-dimensional systems our estimates for the critical couplings are more than two orders of magnitude more accurate than existing estimates. In two and three dimensions we are unaware of any other results for the critical couplings.

Original languageEnglish (US)
Pages (from-to)8945-8958
Number of pages14
JournalPhysical Review B - Condensed Matter and Materials Physics
Issue number14
StatePublished - 1997

ASJC Scopus subject areas

  • Electronic, Optical and Magnetic Materials
  • Condensed Matter Physics

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