Ground State Entropy of Potts Antiferromagnets on Homeomorphic Families of Strip Graphs

Details Ground State Entropy of Potts Antiferromagnets on Homeomorphic Families of Strip Graphs Ground State Entropy of Potts Antiferromagnets on Homeomorphic Families of Strip Graphs

1998-07-07

arxiv.org/abs/cond-mat/9807105v1

Physica A259, 315 (1998)

Physics

Condensed Matter

Statistical Mechanics

42 pages, Latex, 11 encapsulated postscript figures, Physica A, in press

Scientific paper

We present exact calculations of the zero-temperature partition function, and ground-state degeneracy (per site), $W$, for the $q$-state Potts antiferromagnet on a variety of homeomorphic families of planar strip graphs $G = (Ch)_{k_1,k_2,\Sigma,k,m}$, where $k_1$, $k_2$, $\Sigma$, and $k$ describe the homeomorphic structure, and $m$ denotes the length of the strip. Several different ways of taking the total number of vertices to infinity, by sending (i) $m \to \infty$ with $k_1$, $k_2$, and $k$ fixed; (ii) $k_1$ and/or $k_2 \to \infty$ with $m$, and $k$ fixed; and (iii) $k \to \infty$ with $m$ and $p=k_1+k_2$ fixed are studied and the respective loci of points ${\cal B}$ where $W$ is nonanalytic in the complex $q$ plane are determined. The ${\cal B}$'s for limit (i) are comprised of arcs which do not enclose regions in the $q$ plane and, for many values of $p$ and $k$, include support for $Re(q) < 0$. The ${\cal B}$ for limits (ii) and (iii) is the unit circle $|q-1|=1$.

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