Ground State Entropy of Potts Antiferromagnets on Cyclic Polygon Chain Graphs

Abstract

We present exact calculations of chromatic polynomials for families of cyclic graphs consisting of linked polygons, where the polygons may be adjacent or separated by a given number of bonds. From these we calculate the (exponential of the) ground state entropy, $W$, for the q-state Potts model on these graphs in the limit of infinitely many vertices. A number of properties are proved concerning the continuous locus, $\mathcal{B}$, of nonanalyticities in $W$. Our results provide further evidence for a general rule concerning the maximal region in the complex q plane to which one can analytically continue from the physical interval where $S_0>0$.

27 pages, Latex, 17 figs. J. Phys. A, in press

References in corpus (1)

• Ground State Entropy of the Potts Antiferromagnet on Cyclic Strip Graphs

Cited by in corpus (25)

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• Transfer Matrices and Partition-Function Zeros for Antiferromagnetic Potts Models I. General Theory and Square-Lattice Chromatic Polynomial
• Thin Fisher Zeroes
• Exact Potts Model Partition Functions on Wider Arbitrary-Length Strips of the Square Lattice
• T=0 Partition Functions for Potts Antiferromagnets on Square Lattice Strips with (Twisted) Periodic Boundary Conditions
• Structural Properties of Potts Model Partition Functions and Chromatic Polynomials for Lattice Strips
• Ground State Entropy of the Potts Antiferromagnet on Strips of the Square Lattice
• Exact Potts Model Partition Functions on Strips of the Honeycomb Lattice
• $q$-Plane Zeros of the Potts Partition Function on Diamond Hierarchical Graphs
• Zeros of Jones Polynomials for Families of Knots and Links
• Potts Model Partition Functions for Self-Dual Families of Strip Graphs
• Ground State Entropy of the Potts Antiferromagnet with Next-Nearest-Neighbor Spin-Spin Couplings on Strips of the Square Lattice
• T=0 Partition Functions for Potts Antiferromagnets on Lattice Strips with Fully Periodic Boundary Conditions
• Ground State Entropy of the Potts Antiferromagnet on Triangular Lattice Strips
• Exact T=0 Partition Functions for Potts Antiferromagnets on Sections of the Simple Cubic Lattice
• A motivic approach to phase transitions in Potts models
• Exact Potts/Tutte Polynomials for Polygon Chain Graphs
• Chromatic Polynomials for Lattice Strips with Cyclic Boundary Conditions
• Transfer Matrices for the Zero-Temperature Potts Antiferromagnet on Cyclic and Mobius Lattice Strips
• Exact Chromatic Polynomials for Toroidal Chains of Complete Graphs
• The Structure of Chromatic Polynomials of Planar Triangulation Graphs and Implications for Chromatic Zeros and Asymptotic Limiting Quantities
• Potts Partition Function Zeros and Ground State Entropy on Hanoi Graphs
• Exact Potts/Tutte Polynomials for Hammock Chain Graphs
• Jones Polynomials and their Zeros for a Family of Knots and Links
• Chromatic Zeros on the Limit $G_{\infty }^{(p,\ell )}$ of the Family $G_m^{(p,\ell )}$ of Hierarchical Graphs