Ground State Entropy of Potts Antiferromagnets: Homeomorphic Classes with Noncompact W Boundaries

Abstract

We present exact calculations of the zero-temperature partition function $Z(G,q,T=0)$ and ground-state degeneracy $W(\{G\},q)$ for the $q$-state Potts antiferromagnet on a number of families of graphs $G$ for which (generalizing $q$ from ${\mathbb{Z}}_{+}$ to $\mathbb{C}$) the boundary $\mathcal{B}$ of regions of analyticity of $W$ in the complex $q$ plane is noncompact, passing through $z=1/q=0$. For these types of graphs, since the reduced function $W_{red.}=q^{-1}W$ is nonanalytic at $z=0$, there is no large--$q$ Taylor series expansion of $W_{red.}$. The study of these graphs thus gives insight into the conditions for the validity of the large--$q$ expansions. It is shown how such (families of) graphs can be generated from known families by homeomorphic expansion.

37 pages, Latex with encapsulated postscript figures, Physica A, in press

References in corpus (10)

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• Chromatic Polynomials, Potts Models and All That
• Structural Properties of Potts Model Partition Functions and Chromatic Polynomials for Lattice Strips
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• Ground-State Degeneracy of Potts Antiferromagnets on Two-Dimensional Lattices: Approach Using Infinite Cyclic Strip Graphs
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• 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
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• Potts Model Partition Functions for Self-Dual Families of Strip Graphs
• 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
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• The Structure of Chromatic Polynomials of Planar Triangulation Graphs and Implications for Chromatic Zeros and Asymptotic Limiting Quantities
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• 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
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