Exact Potts Model Partition Functions for Strips of the Triangular Lattice

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dc.contributor.author Chang, Shu-Chiuan
dc.contributor.author Jacobsen, Jesper Lykke
dc.contributor.author Salas Martínez, Jesús
dc.contributor.author Shrock, Robert
dc.date.accessioned 2021-07-15T09:53:34Z
dc.date.available 2021-07-15T09:53:34Z
dc.date.issued 2004-02
dc.identifier.bibliographicCitation Chang, S. C., Jacobsen, J. L., Salas, J. & Shrock, R. (2004). Exact Potts Model Partition Functions for Strips of the Triangular Lattice. Journal of Statistical Physics, 114(3-4), pp. 763–823.
dc.identifier.issn 0022-4715
dc.identifier.uri http://hdl.handle.net/10016/33069
dc.description.abstract We present exact calculations of the Potts model partition function Z(G,q,v) for arbitrary q and temperature-like variable v on n-vertex strip graphs G of the triangular lattice for a variety of transverse widths equal to L vertices and for arbitrarily great length equal to m vertices, with free longitudinal boundary conditions and free and periodic transverse boundary conditions. These partition functions have the form Z(G,q,v)=∑NZ,G,λj=1 c z,G,j (λ z,G,j )m-1. We give general formulas for N Z,G,j and its specialization to v=−1 for arbitrary L. The free energy is calculated exactly for the infinite-length limit of the graphs, and the thermodynamics is discussed. It is shown how the internal energy calculated for the case of cylindrical boundary conditions is connected with critical quantities for the Potts model on the infinite triangular lattice. Considering the full generalization to arbitrary complex q and v, we determine the singular locus B, arising as the accumulation set of partition function zeros as m→∞, in the q plane for fixed v and in the v plane for fixed q. Explicit results for partition functions are given in the text for L=3 (free) and L=3, 4 (cylindrical), and plots of partition function zeros and their asymptotic accumulation sets are given for L up to 5. A new estimate for the phase transition temperature of the q=3 Potts antiferromagnet on the 2D triangular lattice is given.
dc.format.extent 61
dc.language.iso eng
dc.publisher Springer
dc.rights © 2004, Plenum Publishing Corporation
dc.subject.other Potts model
dc.subject.other Triangular lattice
dc.subject.other Exact solutions
dc.subject.other Transfer matrix
dc.subject.other Fortuin-Kasteleyn representation
dc.subject.other Tutte polynomial
dc.title Exact Potts Model Partition Functions for Strips of the Triangular Lattice
dc.type article
dc.subject.eciencia Ingeniería Industrial
dc.subject.eciencia Matemáticas
dc.identifier.doi http://dx.doi.org/10.1023/B:JOSS.0000012508.58718.83
dc.rights.accessRights openAccess
dc.type.version acceptedVersion
dc.identifier.publicationfirstpage 763
dc.identifier.publicationissue 3-4
dc.identifier.publicationlastpage 823
dc.identifier.publicationtitle Journal of Statistical Physics
dc.identifier.publicationvolume 114
dc.identifier.uxxi AR/0000001994
dc.affiliation.dpto UC3M. Departamento de Matemáticas
dc.affiliation.grupoinv UC3M. Grupo de Investigación: Modelización, Simulación Numérica y Matemática Industrial
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