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The Blume–Capel model for spins S=1 and 3∕2 in dimensions d=2 and 3

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  • Butera, P.
  • Pernici, M.

Abstract

Expansions through the 24th order at high-temperature and up to 11th order at low-temperature are derived for the main observables of the Blume–Capel model on bipartite lattices (sq,sc and bcc) in 2d and 3d with various values of the spin and in presence of a magnetic field. All expansion coefficients are computed exactly as functions of the crystal and magnetic fields. Several critical properties of the model are analyzed in the two most studied cases of spin S=1 and S=3∕2.

Suggested Citation

  • Butera, P. & Pernici, M., 2018. "The Blume–Capel model for spins S=1 and 3∕2 in dimensions d=2 and 3," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 507(C), pages 22-66.
    • Handle: RePEc:eee:phsmap:v:507:y:2018:i:c:p:22-66
    DOI: 10.1016/j.physa.2018.05.010
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    References listed on IDEAS

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    1. Özkan, A. & Seferoğlu, N. & Kutlu, B., 2006. "Critical exponents of the three-dimensional Blume–Capel model on a cellular automaton," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 362(2), pages 327-337.
    2. Costabile, Emanuel & Roberto Viana, J. & Ricardo de Sousa, J. & Plascak, J.A., 2014. "The general-spin Blume–Capel model: A study of the multicritical behavior using effective-field theory," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 393(C), pages 297-303.
    3. Moonjung Jung & Dong-Hee Kim, 2017. "First-order transitions and thermodynamic properties in the 2D Blume-Capel model: the transfer-matrix method revisited," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 90(12), pages 1-10, December.
    4. Ilkovič, V., 1996. "Cluster expansion for the spin-32 Blume-Capel model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 234(1), pages 545-553.
    5. Butera, P. & Pernici, M., 2016. "Ising low-temperature polynomials and hard-sphere gases on cubic lattices of general dimension," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 444(C), pages 220-234.
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