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Zeros of the Potts Model Partition Function in the Large-$q$ Limit

Chang, Shu-Chiuan ; Shrock, Robert

Int. J. Mod. Phys. B21, 979-994 (2007) [Periódico revisado por pares]

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  • Título:
    Zeros of the Potts Model Partition Function in the Large-$q$ Limit
  • Autor: Chang, Shu-Chiuan ; Shrock, Robert
  • Assuntos: Condensed Matter - Statistical Mechanics
  • É parte de: Int. J. Mod. Phys. B21, 979-994 (2007)
  • Descrição: We study the zeros of the $q$-state Potts model partition function $Z(\Lambda,q,v)$ for large $q$, where $v$ is the temperature variable and $\Lambda$ is a section of a regular $d$-dimensional lattice with coordination number $\kappa_\Lambda$ and various boundary conditions. We consider the simultaneous thermodynamic limit and $q \to \infty$ limit and show that when these limits are taken appropriately, the zeros lie on the unit circle $|x_\Lambda|=1$ in the complex $x_\Lambda$ plane, where $x_\Lambda=v q^{-2/\kappa_\Lambda}$. For large finite sections of some lattices we also determine the circular loci near which the zeros lie for large $q$. Comment: 11 pages, revtex, 16 eps figures

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