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Square-lattice random potts model: Criticality and pitchfork bifurcation

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  • Costa, Uriel M.S.
  • Tsallis, Constantino

Abstract

Within a real space renormalization group framework based on self-dual clusters, we discuss the criticality of the quenched bond-mixed q-state Potts ferromagnet on a square lattice. On qualitative grounds we exhibit that crossover from the pure fixed point to the random one occurs, while q increases, through a pitchfork bifurcation; the relationship with the Harris criterion is analyzed. On quantitative grounds we present high precision numerical values for the critical temperatures corresponding to various concentrations of the coupling constants J1 and J2, and various ratios J1/J2. The pure, random and crossover critical exponents are discussed as well.

Suggested Citation

  • Costa, Uriel M.S. & Tsallis, Constantino, 1984. "Square-lattice random potts model: Criticality and pitchfork bifurcation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 128(1), pages 207-228.
    • Handle: RePEc:eee:phsmap:v:128:y:1984:i:1:p:207-228
    DOI: 10.1016/0378-4371(84)90088-8
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    1. Stinchcombe, Arthur L., 1976. "Rules and Laws in Sociology. By Robert Brown. (Chicago: Aldine, 1973. Pp. x, 181. $7.95.)," American Political Science Review, Cambridge University Press, vol. 70(1), pages 199-200, March.
    2. Apthorpe, Raymond, 1979. "The burden of land reform in Taiwan: An Asian model land reform re-analysed," World Development, Elsevier, vol. 7(4-5), pages 519-530.
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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.

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