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    One-dimensional Potts model, Lee-Yang edges, and chaos


    Dolan, Brian P. and Johnston, D.A. (2002) One-dimensional Potts model, Lee-Yang edges, and chaos. Physical Review E, 65 (057103). pp. 1-4. ISSN 1539-3755

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    Abstract

    It is known that the exact renormalization transformations for the one-dimensional Ising model in a field can be cast in the form of the logistic map f (x)54x(12x) with x a function of the Ising couplings K and h. The locus of the Lee-Yang zeros for the one-dimensional Ising model in the K,h plane is given by the Julia set of the logistic map. In this paper we show that the one-dimensional q-state Potts model for q>1 also displays such behavior. A suitable combination of couplings, which reduces to the Ising case for q52, can again be used to define an x satisfying f (x)54x(12x). The Lee-Yang zeros no longer lie on the unit circle in the complex z5eh plane for qÞ2, but their locus still maps onto the Julia set of the logistic map.

    Item Type: Article
    Additional Information: The definitive version of this article is available at One-dimensional Potts model, Lee-Yang edges, and chaos Brian P. Dolan and D. A. Johnston Phys. Rev. E 65, 057103 (2002) – Published 14 May 2002. B.D. was partially supported by Enterprise Ireland Basic Research Grant No. SC/1998/739 and B.D. and D.J. by an Enterprise Ireland/British Council Research Visits Scheme Grant No. BC/2000/004. B.D. would like to thank Heriot- Watt Mathematics Department for its hospitality and D.J. would like to thank the Department of Mathematical Physics, National University of Ireland, Maynooth for the same.
    Keywords: One-dimensional Potts model; Lee-Yang edges; chaos; Ising model;
    Academic Unit: Faculty of Science and Engineering > Mathematical Physics
    Item ID: 5928
    Identification Number: https://doi.org/10.1103/PhysRevE.65.057103
    Depositing User: Dr. Brian Dolan
    Date Deposited: 02 Mar 2015 16:54
    Journal or Publication Title: Physical Review E
    Publisher: American Physical Society
    Refereed: Yes
    Funders: Enterprise Ireland (EI), British Council
    URI:

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