Ground State Entropy of Potts Antiferromagnets: Cases with Noncompact W Boundaries Having Multiple Points at 1/q = 0

Abstract

We present exact calculations of the zero-temperature partition function, $Z(G,q,T=0)$, and ground-state degeneracy (per site), $W(G,q)$, for the $q$-state Potts antiferromagnet on a number of families of graphs $G$ for which the boundary $\mathcal{B}$ of regions of analyticity of $W$ in the complex $q$ plane is noncompact and has the properties that (i) in the $z=1/q$ plane, the point $z=0$ is a multiple point on $\mathcal{B}$ and (ii) $\mathcal{B}$ includes support for $Re(q)<0$. These families are generated by the method of homeomorphic expansion. Our results give further insight into the conditions for the validity of large--$q$ series expansions for the reduced function $W_{red.}=q^{-1}W$.

29 pages, Latex, 10 encapsulated postscript figures, J. Phys. A, in press

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Cited by in corpus (29)

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• A Little Statistical Mechanics for the Graph Theorist
• Exact Potts Model Partition Functions on Wider Arbitrary-Length Strips of the Square Lattice
• Exact Potts Model Partition Function on Strips of the Triangular Lattice
• Chromatic Polynomials, Potts Models and All That
• Ground State Entropy of Potts Antiferromagnets: Homeomorphic Classes with Noncompact W Boundaries
• Structural Properties of Potts Model Partition Functions and Chromatic Polynomials for Lattice Strips
• Ground-State Degeneracy of Potts Antiferromagnets on Two-Dimensional Lattices: Approach Using Infinite Cyclic Strip Graphs
• Ground State Entropy of the Potts Antiferromagnet on Strips of the Square Lattice
• Ground State Entropy of the Potts Antiferromagnet on Cyclic Strip Graphs
• Ground State Entropy of Potts Antiferromagnets on Cyclic Polygon Chain Graphs
• 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
• 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
• Graph polynomials and their applications I: The Tutte polynomial
• 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
• Transfer matrices and partition-function zeros for antiferromagnetic Potts models. VI. Square lattice with special boundary conditions
• Linear bound in terms of maxmaxflow for the chromatic roots of series-parallel graphs
• Chromatic Polynomials for Lattice Strips with Cyclic Boundary Conditions
• 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
• Lower Bounds on the Ground State Entropy of the Potts Antiferromagnet on Slabs of the Simple Cubic Lattice
• Ground State Entropy of the Potts Antiferromagnet on Homeomorphic Expansions of Kagome Lattice Strips
• Improved Lower Bounds on the Ground-State Entropy of the Antiferromagnetic Potts Model
• Exact Potts/Tutte Polynomials for Hammock Chain Graphs