Partition function zeros of the Q-state Potts model on the simple-cubic lattice

Abstract

The $Q$-state Potts model on the simple-cubic lattice is studied using the zeros of the exact partition function on a finite lattice. The critical behavior of the model in the ferromagnetic and antiferromagnetic phases is discussed based on the distribution of the zeros in the complex temperature plane. The characteristic exponents at complex-temperature singularities, which coexist with the physical critical points in the complex temperature plane for no magnetic field ($H_q=0$), are estimated using the low-temperature series expansion. We also study the partition function zeros of the Potts model for nonzero magnetic field. For $H_q>0$ the physical critical points disappear and the Fisher edge singularities appear in the complex temperature plane. The characteristic exponents at the Fisher edge singularities are calculated using the high-field, low-temperature series expansion. It seems that the Fisher edge singularity is related to the Yang-Lee edge singularity which appears in the complex magnetic-field plane for $T>T_c$.

26 pages, 4 figures

References in corpus (1)

• Density of states, Potts zeros, and Fisher zeros of the Q-state Potts model for continuous Q

Cited by in corpus (7)

• Finite density QCD via imaginary chemical potential
• Statistical Mechanics of Equilibrium and Nonequilibrium Phase Transitions: The Yang-Lee Formalism
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• Density of Yang-Lee zeros in the thermodynamic limit from tensor network methods
• Yang-Lee zeros and the critical behavior of the infinite-range two- and three-state Potts models
• Lattice QCD at finite density: imaginary chemical potential