The 3-edge-colouring problem on the 4-8 and 3-12 lattices
| Autor: | Fjaerestad, J. O. |
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| Rok vydání: | 2009 |
| Předmět: | |
| Zdroj: | J. Stat. Mech. (2010) P01004 |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1088/1742-5468/2010/01/P01004 |
| Popis: | We consider the problem of counting the number of 3-colourings of the edges (bonds) of the 4-8 lattice and the 3-12 lattice. These lattices are Archimedean with coordination number 3, and can be regarded as decorated versions of the square and honeycomb lattice, respectively. We solve these edge-colouring problems in the infinite-lattice limit by mapping them to other models whose solution is known. The colouring problem on the 4-8 lattice is mapped to a completely packed loop model with loop fugacity n=3 on the square lattice, which in turn can be mapped to a six-vertex model. The colouring problem on the 3-12 lattice is mapped to the same problem on the honeycomb lattice. The 3-edge-colouring problems on the 4-8 and 3-12 lattices are equivalent to the 3-vertex-colouring problems (and thus to the zero-temperature 3-state antiferromagnetic Potts model) on the "square kagome" ("squagome") and "triangular kagome" lattices, respectively. Comment: 10 pages, 4 figures (2 in colour). Added discussion, 2 refs. in Sec. 4 |
| Databáze: | arXiv |
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