Study of the Potts Model on the Honeycomb and Triangular Lattices: Low-Temperature Series and Partition Function Zeros

Abstract

We present and analyze low-temperature series and complex-temperature partition function zeros for the $q$-state Potts model with $q=4$ on the honeycomb lattice and $q=3,4$ on the triangular lattice. A discussion is given as to how the locations of the singularities obtained from the series analysis correlate with the complex-temperature phase boundary. Extending our earlier work, we include a similar discussion for the Potts model with $q=3$ on the honeycomb lattice and with $q=3,4$ on the kagomé lattice.

33 pages, Latex, 9 encapsulated postscript figures, J. Phys. A, in press

References in corpus (19)

• Absence of Phase Transition for Antiferromagnetic Potts Models via the Dobrushin Uniqueness Theorem
• Asymptotic Limits and Zeros of Chromatic Polynomials and Ground State Entropy of Potts Antiferromagnets
• Kac-Moody Symmetries of Critical Ground States
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• Zeros of the Partition Function for Higher--Spin 2D Ising Models
• Complex-Temperature Partition Function Zeros of the Potts Model on the Honeycomb and Kagomé Lattices
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• Low temperature series expansions for the square lattice Ising model with spin S > 1
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Cited by in corpus (18)

• Statistical Mechanics of Equilibrium and Nonequilibrium Phase Transitions: The Yang-Lee Formalism
• Transfer Matrices and Partition-Function Zeros for Antiferromagnetic Potts Models I. General Theory and Square-Lattice Chromatic Polynomial
• Exact Potts Model Partition Functions on Ladder Graphs
• Spanning forests and the q-state Potts model in the limit q \to 0
• Yang-Lee zeros of the Q-state Potts model in the complex magnetic-field plane
• Exact Potts Model Partition Function on Strips of the Triangular Lattice
• Exact Potts Model Partition Functions on Strips of the Honeycomb Lattice
• Complex-Temperature Phase Diagrams for the q-State Potts Model on Self-Dual Families of Graphs and the Nature of the $q\to \infty$ Limit
• Zeros of Jones Polynomials for Families of Knots and Links
• Fisher zeros of the Q-state Potts model in the complex temperature plane for nonzero external magnetic field
• Reliability Polynomials and their Asymptotic Limits for Families of Graphs
• Potts correlators and the static three-quark potential
• Exact Results for Average Cluster Numbers in Bond Percolation on Lattice Strips
• On zero-free regions for the anti-ferromagnetic Potts model on bounded-degree graphs
• Partition Function Zeros of a Restricted Potts Model on Lattice Strips and Effects of Boundary Conditions
• Changeover phenomenon in randomly colored Potts models
• Potts Partition Function Zeros and Ground State Entropy on Hanoi Graphs
• Ground State Entropy in Potts Antiferromagnets and Chromatic Polynomials