Exact Potts model partition functions for strips of the triangular lattice

Shu Chiuan Chang, Jesper Lykke Jacobsen, Jesús Salas, Robert Shrock

研究成果: Article同行評審

31 引文 斯高帕斯(Scopus)

摘要

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) = ∑j = 1 N Z,G,λ cZ,G,jZ,G,j) m-1. We give general formulas for NZ,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.

原文English
頁(從 - 到)763-823
頁數61
期刊Journal of Statistical Physics
114
發行號3-4
DOIs
出版狀態Published - 2004 2月

All Science Journal Classification (ASJC) codes

  • 統計與非線性物理學
  • 數學物理學

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