End Graph Effects on Chromatic Polynomials for Strip Graphs of Lattices and their Asymptotic Limits

Abstract

We report exact calculations of the ground state degeneracy per site (exponent of the ground state entropy) $W(\{G\},q)$ of the $q$-state Potts antiferromagnet on infinitely long strips with specified end graphs for free boundary conditions in the longitudinal direction and free and periodic boundary conditions in the transverse direction. This is equivalent to calculating the chromatic polynomials and their asymptotic limits for these graphs. Making the generalization from $q\in {\mathbb{Z}}_{+}$ to $q\in \mathbb{C}$, we determine the full locus $\mathcal{B}$ on which $W$ is nonanalytic in the complex $q$ plane. We report the first example for this class of strip graphs in which $\mathcal{B}$ encloses regions even for planar end graphs. The bulk of the specific strip graph that exhibits this property is a part of the $(3^3\cdot 4^2)$ Archimedean lattice.

27 pages, Revtex, 11 encapsulated postscript figures, Physica A, in press

References in corpus (4)

• Chromatic Polynomials for Families of Strip Graphs and their Asymptotic Limits
• Lower Bounds and Series for the Ground State Entropy of the Potts Antiferromagnet on Archimedean Lattices and their Duals
• Chromatic Polynomials for $J(\prod H)I$ Strip Graphs and their Asymptotic Limits
• Ground State Entropy of Potts Antiferromagnets on Homeomorphic Families of Strip Graphs

Cited by in corpus (2)

• Transfer Matrices and Partition-Function Zeros for Antiferromagnetic Potts Models I. General Theory and Square-Lattice Chromatic Polynomial
• Chromatic Polynomials for $J(\prod H)I$ Strip Graphs and their Asymptotic Limits