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Ground State Entropy of Potts Antiferromagnets: Homeomorphic Classes with Noncompact W Boundaries | | Robert Shrock
; Shan-Ho Tsai
; | | Date: |
30 Nov 1998 | | Journal: | Physica A265, 186 (1999) | | Subject: | Statistical Mechanics; Combinatorics | cond-mat.stat-mech hep-lat math.CO | | 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 ${cal B}$ 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. | | Source: | arXiv, cond-mat/9811410 | | Services: | Forum | Review | PDF | Favorites | |
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