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Critical Behavior of the Blume-Emery-Griffiths Model for a Simple Cubic Lattice on the Cellular Automaton

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Abstract

The spin-1 Ising model with the nearest-neighbour bilinear and biquadratic interactions and single-ion anisotropy is simulated on a cellular automaton which improved from the Creutz cellular automaton (CCA) for a simple cubic lattice. The simulations have been made for several k=K/J and d=D/J in the 0≤d<3 and −2≤k≤0 parameter regions. We confirm the existence of the re-entrant and the successive re-entrant phase transitions near the phase boundary. The phase diagrams characterizing phase transitions are presented for comparison with those obtained from other calculations. The static critical exponents are estimated within the framework of the finite-size scaling theory at d=0, 1 and 2 in the interval −2≤k≤0. The results are compatible with the universal Ising critical behavior.

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Authors and Affiliations

  1. Fen Bilimleri Enstitüsü, Fizik Anabilim Dalı, Gazi Üniversitesi, Ankara, Turkey

    N. Seferoğlu

  2. Fen-Edebiyat Fakültesi, Fizik Bölümü, Gazi Üniversitesi, 06500 Teknikokullar, Ankara, Turkey

    B. Kutlu

Authors
  1. N. Seferoğlu
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  2. B. Kutlu
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Correspondence to N. Seferoğlu.

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Seferoğlu, N., Kutlu, B. Critical Behavior of the Blume-Emery-Griffiths Model for a Simple Cubic Lattice on the Cellular Automaton. J Stat Phys 129, 453–468 (2007). https://doi.org/10.1007/s10955-007-9392-z

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  • DOI: https://doi.org/10.1007/s10955-007-9392-z

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