IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v112y1982i3p405-465.html
   My bibliography  Save this article

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

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/037843718290187X
    Download Restriction: Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000
    File URL: https://libkey.io/10.1016/0378-4371(82)90187-X?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Office of Health Economics, 1977. "Preventing Bronchitis," Series on Health 000275, Office of Health Economics.
    2. Holloway, Wilfred B., 1980. "Federal intervention and youth programs: An essay on the viability of the in-school work experience/education model," Children and Youth Services Review, Elsevier, vol. 2(1-2), pages 81-96.
    3. 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.
    4. Schick, GJ & Stroup, JW, 1981. "Experience with a multi-year fleet planning model," Omega, Elsevier, vol. 9(4), pages 389-396.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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, 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.
    4. 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.
    5. 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.
    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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. 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.
    2. 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.
    3. Rosskopf, Michael & Lehner, Stephan & Gollnick, Volker, 2014. "Economic–environmental trade-offs in long-term airline fleet planning," Journal of Air Transport Management, Elsevier, vol. 34(C), pages 109-115.
    4. Igloi, F. & Vanderzande, C., 1986. "Renormalisation group study of the (2+1) dimensional Potts model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 135(2), pages 347-358.
    5. Geursen, Izaak L. & Santos, Bruno F. & Yorke-Smith, Neil, 2023. "Fleet planning under demand and fuel price uncertainty using actor–critic reinforcement learning," Journal of Air Transport Management, Elsevier, vol. 109(C).
    6. Wang, Jian-Sheng & Nielaba, Peter & Privman, Vladimir, 1993. "Locally frozen defects in random sequential adsorption with diffusional relaxation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 199(3), pages 527-538.
    7. Bernie O'Brien, 1984. "Patterns of European Diagnoses and Prescribing," Monograph 000344, Office of Health Economics.
    8. Du, Jia Yan & Brunner, Jens O. & Kolisch, Rainer, 2016. "Obtaining the optimal fleet mix: A case study about towing tractors at airports," Omega, Elsevier, vol. 64(C), pages 102-114.
    9. Ceder, G. & Dreyssé, H. & de Fontaine, D., 1993. "Triplet interactions and the c(2×2) overlayer phase diagram," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 193(1), pages 105-113.
    10. 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.
    11. 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.
    12. Zhang, Haiyan & Xu, Bowei, 1994. "Conformal theory of a next-nearest-neighbour interaction model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 202(1), pages 291-300.
    13. 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.
    14. 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.
    15. Sa, Constantijn A.A. & Santos, Bruno F. & Clarke, John-Paul B., 2020. "Portfolio-based airline fleet planning under stochastic demand," Omega, Elsevier, vol. 97(C).
    16. Meir, Yigal & Aharony, Amnon, 1989. "Viscous fingers on fractals," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 157(1), pages 524-528.
    17. Barber, Michael N., 1985. "Phenomenological renormalization of multi-parameter systems," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 130(1), pages 171-193.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:phsmap:v:112:y:1982:i:3:p:405-465. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.journals.elsevier.com/physica-a-statistical-mechpplications/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.