Partition function zeros of the Q-state Potts model for non-integer Q

Abstract

The distribution of the zeros of the partition function in the complex temperature plane (Fisher zeros) of the two-dimensional Q-state Potts model is studied for non-integer Q. On $L\times L$ self-dual lattices studied ($L\le 8$), no Fisher zero lies on the unit circle $p_0=e^{i\theta }$ in the complex $p=(e^{\beta J}-1)/\sqrt{Q}$ plane for Q<1, while some of the Fisher zeros lie on the unit circle for Q>1 and the number of such zeros increases with increasing Q. The ferromagnetic and antiferromagnetic properties of the Potts model are investigated using the distribution of the Fisher zeros. For the Potts ferromagnet we verify the den Nijs formula for the thermal exponent $y_t$. For the Potts antiferromagnet we also verify the Baxter conjecture for the critical temperature and present new results for the thermal exponents in the range 0<Q<3.

12 pages, 7 figures, RevTeX

References in corpus (1)

• Antiferromagnetic Potts Models on the Square Lattice

Cited by in corpus (8)

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• Partition function zeros of the Q-state Potts model on the simple-cubic lattice
• Yang-Lee Zeros of the Q-state Potts Model on Recursive Lattices
• Complex-q zeros of the partition function of the Potts model with long-range interactions
• Transfer-matrix approach to the three-dimensional bond percolation: An application of Novotny's formalism