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Application of the renormalization group method to the s = 12XY model on the triangular lattice

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  • Rogiers, J.
  • Betts, D.D.

Abstract

The two-dimensional spin one half XY model may undergo an unusual type of phase transition. A formulation of the renormalization group approach of Niemeijer and van Leeuwen suitable for quantum-mechanical systems is presented. The method is applied to the spin one half XY model on the triangular lattice using a second order cumulant expansion based on division of the triangular lattice into seven spin cells. The resulting free energy curve is in excellent agreement with that obtained from the high temperature series expansion. An unstable fixed point is found but the corresponding critical temperature is not in good agreement with the series expansion value. Pathological values are found for the critical exponents.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:phsmap:v:85:y:1976:i:3:p:553-565
    DOI: 10.1016/0378-4371(76)90024-8
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    References listed on IDEAS

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    1. Dekeyser, R. & Reynaert, M., 1976. "The XY-model and the self-avoiding walk approximation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 84(1), pages 197-204.
    2. 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.
    3. Kondo, Osamu, 1973. "Hiroshi Fukazawa, Studies in the Socio-Economic History of India," Economic Review, Hitotsubashi University, vol. 24(4), pages 385-387, October.
    4. Seymour Kaplan, 1966. "Solution of the Lorie-Savage and Similar Integer Programming Problems by the Generalized Lagrange Multiplier Method," Operations Research, INFORMS, vol. 14(6), pages 1130-1136, December.
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    Cited by:

    1. Hu, Bambi, 1979. "Renormalization group study of the one dimensional quantum mechanical XY model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 99(1), pages 330-336.

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