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Ground State Entropy of Potts Antiferromagnets: Cases with Noncompact W Boundaries Having Multiple Points at 1/q = 0 | | Robert Shrock
; Shan-Ho Tsai
; | | Date: |
6 Oct 1998 | | Journal: | J. Phys. A 31, 9641 (1998) | | 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 (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 $W_{red.}=q^{-1}W$. | | Source: | arXiv, cond-mat/9810057 | | Services: | Forum | Review | PDF | Favorites | |
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