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The Kadanoff lowerbound renormalization transformation for the q-state Potts model

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  • Den Nijs, M.P.M.

Abstract

The Kadanoff lowerbound renormalization transformation when applied to the 2-dimensional q-state Potts model, is found to show a bifurcation phenomenon at q = 4, that might be considered as signalling the onset to the first-order transition. At the value of the free parameter where the bifurcation is found, the specific heat exponent takes almost the value predicted by weak universality α(4) = 23, while the cross-over exponent in the Potts-lattice gas direction becomes marginal. The cross-over exponent in the cubic direction is found already to be irrelevant for q > 3.3. Further a duality relation for a class of models obtained by a partial breaking of the Potts symmetry in the hamiltonian, including the cubic model is derived.

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  • Den Nijs, M.P.M., 1979. "The Kadanoff lowerbound renormalization transformation for the q-state Potts model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 95(3), pages 449-472.
    • Handle: RePEc:eee:phsmap:v:95:y:1979:i:3:p:449-472
    DOI: 10.1016/0378-4371(79)90026-8
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    References listed on IDEAS

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    1. Office of Health Economics, 1977. "Preventing Bronchitis," Series on Health 000275, Office of Health Economics.
    2. Den Nijs, M.P.M. & Pruisken, A.M.M. & Van Leeuwen, J.M.J., 1976. "Critical phenomena for a triangular spin lattice I," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 84(3), pages 539-556.
    3. Knops, H.J.F., 1977. "On Kadanoff's approximate renormalization group transformation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 86(2), pages 448-456.
    4. Van Saarloos, W. & Van Leeuwen, J.M.J. & Pruisken, A.M.M., 1978. "Variational principles in renormalization theory," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 92(3), pages 323-342.
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    Cited by:

    1. Mariz, A.M. & Nobre, F.D. & de Souza, E.S., 1991. "Criticality of the bond-diluted Z(4) ferromagnet on the square lattice," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 178(2), pages 364-375.
    2. Taggart, G.Bruce, 1982. "Correlated effective field approximation for the dilute Ising ferromagnet," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 116(1), pages 34-44.
    3. 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.
    4. Chame, Anna & Tsallis, Constantino, 1990. "Criticality of the discrete N-vector ferromagnet in a cubic lattice with a free surface," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 165(1), pages 41-63.
    5. Kim, Doochul, 1984. "Self-dual transfer matrix renormalization for the triangular Potts model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 123(2), pages 577-585.
    6. Meir, Yigal & Aharony, Amnon, 1989. "Viscous fingers on fractals," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 157(1), pages 524-528.
    7. 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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