Large-[formula presented] series expansion for the ground-state degeneracy of the [formula presented]-state Potts antiferromagnet on the [formula presented] lattice

Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

Volumn 57, Issue 3, 1998, Pages 2686-2689

  Tsai, Shan Ho ^a  

^a STONY BROOK UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0039219950     PISSN: 1063651X     EISSN: None     Source Type: Journal    
DOI: 10.1103/PhysRevE.57.2686     Document Type: Article

References (26)

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25. In Ref. 14 the weights m(Ga, q) are called reduced weights and denoted by w(Ga, q). A total weight is also defined therein. However, in the present paper we shall not refer to the total weight.
26. The expansion of the chromatic polynomial P(G, q) in terms of subgraphs in Eq. (2.7) can be regarded as a special case of the low-temperature series expansion of the partition function of the Potts model on the dual graph D(G) 4. In this formulation, for planar subgraphs Ga, the weights m(Ga, q) in Eq. (2.7) are simply given by m(Ga, q)=P(D(Ga), q)/qe-v+1, where P(D(Ga), q) is the chromatic polynomial on the graph dual to Ga; and e and v are the number of edges and vertices, respectively, of Ga 4. We thank Professor F. Y. Wu for this comment.