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Ising model with two-spin interactions and three-spin interactions on a square lattice

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  • Horiguchi, T.

Abstract

An investigation is given for an Ising model on a square lattice with two-spin interactions for all the vertical bonds and with three-spin interactions which exist alternately from triplets of three successive sites in a row of the horizontal direction and slantwise from row to row. We prove that there exists a phase transition in the system. An upper bound and a lower bound to the critical temperature are obtained. By using the finite-size scaling method, we calculate the thermal exponent and suggest that the system belongs to the same universality class as the Baxter-Wu model.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:phsmap:v:136:y:1986:i:1:p:109-123
    DOI: 10.1016/0378-4371(86)90045-2
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    1. Brückmann, Friedel, 1978. "Investitionsstau: Nicht allein ein ökonomisches Problem," Wirtschaftsdienst – Zeitschrift für Wirtschaftspolitik (1949 - 2007), ZBW - Leibniz Information Centre for Economics, vol. 58(8), pages 405-409.
    2. Blöte, H.W.J & Nightingale, M.P, 1982. "Critical behaviour of the two-dimensional Potts model with a continuous number of states; A finite size scaling analysis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 112(3), pages 405-465.
    3. 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.
    4. Griffiths, Brian, 1972. "The Welfare Cost of the U.K. Clearing Banks' Cartel," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 4(2), pages 227-244, May.
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