Fisher zeros of the Q-state Potts model in the complex temperature plane for nonzero external magnetic field

Abstract

The microcanonical transfer matrix is used to study the distribution of the Fisher zeros of the $Q>2$ Potts models in the complex temperature plane with nonzero external magnetic field $H_q$. Unlike the Ising model for $H_q\ne 0$ which has only a non-physical critical point (the Fisher edge singularity), the $Q>2$ Potts models have physical critical points for $H_q<0$ as well as the Fisher edge singularities for $H_q>0$. For $H_q<0$ the cross-over of the Fisher zeros of the $Q$-state Potts model into those of the ($Q-1$)-state Potts model is discussed, and the critical line of the three-state Potts ferromagnet is determined. For $H_q>0$ we investigate the edge singularity for finite lattices and compare our results with high-field, low-temperature series expansion of Enting. For $3\le Q\le 6$ we find that the specific heat, magnetization, susceptibility, and the density of zeros diverge at the Fisher edge singularity with exponents ${\alpha }_e$, ${\beta }_e$, and ${\gamma }_e$ which satisfy the scaling law ${\alpha }_e+2{\beta }_e+{\gamma }_e=2$.

24 pages, 7 figures, RevTeX, submitted to Physical Review E

References in corpus (4)

• Yang-Lee zeros of the Q-state Potts model in the complex magnetic-field plane
• Study of the Potts Model on the Honeycomb and Triangular Lattices: Low-Temperature Series and Partition Function Zeros
• Complex-Temperature Partition Function Zeros of the Potts Model on the Honeycomb and Kagomé Lattices
• Singular Behaviour of the Potts Model in the Thermodynamic Limit

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• Density of Yang-Lee zeros for the Ising ferromagnet
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• Exact results for the zeros of the partition function of the Potts model on finite lattices
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