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Exact Potts Model Partition Functions for Strips of the Triangular Lattice

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dc.affiliation.dptoUC3M. Departamento de Matemáticases
dc.affiliation.grupoinvUC3M. Grupo de Investigación: Modelización, Simulación Numérica y Matemática Industriales
dc.contributor.authorChang, Shu-Chiuan
dc.contributor.authorJacobsen, Jesper Lykke
dc.contributor.authorSalas Martínez, Jesús
dc.contributor.authorShrock, Robert
dc.date.accessioned2021-07-15T09:53:34Z
dc.date.available2021-07-15T09:53:34Z
dc.date.issued2004-02
dc.description.abstractWe 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.en
dc.format.extent61
dc.identifier.bibliographicCitationChang, 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.en
dc.identifier.doihttp://dx.doi.org/10.1023/B:JOSS.0000012508.58718.83
dc.identifier.issn0022-4715
dc.identifier.publicationfirstpage763
dc.identifier.publicationissue3-4
dc.identifier.publicationlastpage823
dc.identifier.publicationtitleJournal of Statistical Physicsen
dc.identifier.publicationvolume114
dc.identifier.urihttps://hdl.handle.net/10016/33069
dc.identifier.uxxiAR/0000001994
dc.language.isoeng
dc.publisherSpringeren
dc.rights© 2004, Plenum Publishing Corporationen
dc.rights.accessRightsopen accessen
dc.subject.ecienciaIngeniería Industriales
dc.subject.ecienciaMatemáticases
dc.subject.otherPotts modelen
dc.subject.otherTriangular latticeen
dc.subject.otherExact solutionsen
dc.subject.otherTransfer matrixen
dc.subject.otherFortuin-Kasteleyn representationen
dc.subject.otherTutte polynomialen
dc.titleExact Potts Model Partition Functions for Strips of the Triangular Latticeen
dc.typeresearch article*
dc.type.hasVersionAM*
dspace.entity.typePublication
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