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Ising models with two- and three-spin interactions: Mean field equation of state

Author

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  • Frøyen, S.
  • Sudbø, Aa.S.
  • Hemmer, P.C.

Abstract

The Ising model with pair and triplet interactions on the triangular lattice is solved in the mean-field approximation. With a sufficiently strong triplet interaction two first-order transitions take place at low temperature, and at intermediate temperatures one transition, terminating in a critical point. For J2 > 0.75J3 only the latter transition remains.

Suggested Citation

  • Frøyen, S. & Sudbø, Aa.S. & Hemmer, P.C., 1976. "Ising models with two- and three-spin interactions: Mean field equation of state," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 85(2), pages 399-408.
    • Handle: RePEc:eee:phsmap:v:85:y:1976:i:2:p:399-408
    DOI: 10.1016/0378-4371(76)90058-3
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    References listed on IDEAS

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    1. Hemmer Hans-Rimbert & Paul Hans-Joachim, 1974. "Einige Bemerkungen zum Thema: Wachstum, Verteilung und Geldschöpfungsmultiplikator," Journal of Economics and Statistics (Jahrbuecher fuer Nationaloekonomie und Statistik), De Gruyter, vol. 188(5), pages 464-469, April.
    2. Eckstein, Otto & Green, Edward W & Sinai, Allen, 1974. "The Data Resources Model: Uses, Structure, and Analysis of the U.S. Economy," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 15(3), pages 595-615, October.
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    1. Rogiers, J. & Betts, D.D., 1976. "Application of the renormalization group method to the s = 12XY model on the triangular lattice," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 85(3), pages 553-565.
    2. Dóczi-Réger, J. & Hemmer, P.C., 1981. "Second-order phase transitions in triangular ising models with two- and three-spin interactions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 109(3), pages 541-554.
    3. Barber, Michael N., 1985. "Phenomenological renormalization of multi-parameter systems," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 130(1), pages 171-193.
    4. Horiguchi, T., 1986. "Ising model with two-spin interactions and three-spin interactions on a square lattice," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 136(1), pages 109-123.
    5. Horiguchi, T. & Gonçalves, L.L., 1985. "Mixed spin Ising models with two-spin interactions and three-spin interactions of the diced lattice," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 133(3), pages 460-472.

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