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Critical behaviour of the two-dimensional Potts model with a continuous number of states; A finite size scaling analysis

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  • Blöte, H.W.J
  • Nightingale, M.P

Abstract

We investigate the critical behaviour of the two-dimensional, q-state Potts model, using finite-size scaling and transfer matrix methods. For the continuous transition range (04). For completely finite systems, we recover the power law behaviour describe by discontinuity fixed point exponents; however, for systems that are infinite in one direction, exponential behaviour occurs. This is illustrated numerically by the exponential divergences of the susceptibility and specific heat with increasing system size for q⪢4.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:phsmap:v:112:y:1982:i:3:p:405-465
    DOI: 10.1016/0378-4371(82)90187-X
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    References listed on IDEAS

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    Cited by:

    1. B. Zhang & J. Wang & W. Zhang & G. C. Wang, 2020. "Nonlinear Scaling Behavior of Visible Volatility Duration for Financial Statistical Physics Dynamics," Computational Economics, Springer;Society for Computational Economics, vol. 56(2), pages 373-389, August.
    2. Blöte, H.W.J. & Nightingale, M.P., 1985. "Universality in two-dimensional Ising models," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 134(1), pages 274-282.
    3. Blöte, H.W.J. & Capel, H.W., 1986. "Finite-size scaling and the isotropic spin-one antiferromagnetic chain," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 139(2), pages 387-394.
    4. Privman, V., 1984. "Convergence and extrapolation in finite-size scaling renormalization," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 123(2), pages 428-442.
    5. Blöte, Henk W.J. & Nienhuis, Bernard, 1989. "The phase diagram of the O(n) model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 160(2), pages 121-134.
    6. 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.
    7. Dudek, M.R. & Van Leeuwen, J.M.J. & Blöte, H.W.J., 1987. "Convergence of finite size scaling analysis: Weak size dependence of renormalization transformations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 147(1), pages 344-367.

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