Ground State Entropy of the Potts Antiferromagnet on Triangular Lattice Strips
โ Scribed by Shu-Chiuan Chang; Robert Shrock
- Publisher
- Elsevier Science
- Year
- 2001
- Tongue
- English
- Weight
- 227 KB
- Volume
- 290
- Category
- Article
- ISSN
- 0003-4916
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โฆ Synopsis
We present exact calculations of the zero-temperature partition function (chromatic polynomial) P for the q-state Potts antiferromagnet on triangular lattice strips of arbitrarily great length L x vertices and of width L y vertices and, in the L x โ โ limit, the exponent of the ground state entropy, W = e S 0 /k B . The strips considered, with their boundary conditions (BC), are (a) (FBC y , PBC x ) = cyclic for
, and (f) (FBC y , FBC x ) = free, L y = 5, where F, P, and T P denote free, periodic, and twisted periodic. Several interesting features are found, including the presence of terms in P proportional to cos(2ฯ L x /3) for case (c). The continuous locus of points B where W is nonanalytic in the q plane is discussed for each case and a comparative discussion is given of the respective loci B for families with different boundary conditions. Numerical values of W are given for infinite-length strips of various widths and are shown to approach values for the 2D lattice rapidly. A remark is also made concerning a zero-free region for chromatic zeros. Some results are given for strips of other lattices.
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