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

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

1998-10-06

arxiv.org/abs/cond-mat/9810057v1

J. Phys. A 31, 9641 (1998)

Physics

Condensed Matter

Statistical Mechanics

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

Scientific paper

10.1088/0305-4470/31/48/003

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 ${\cal B}$ 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 ${\cal B}$ and (ii) ${\cal B}$ 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 $W_{red.}=q^{-1}W$.

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