The 3-edge-colouring problem on the 4-8 and 3-12 lattices

Fjaerestad, J. O. (2010) The 3-edge-colouring problem on the 4-8 and 3-12 lattices. Journal of Statistical Mechanics: Theory and Experiment, 2010 1: P01004-1-P01004-10. doi:10.1088/1742-5468/2010/01/P01004

Author Fjaerestad, J. O.
Title The 3-edge-colouring problem on the 4-8 and 3-12 lattices
Journal name Journal of Statistical Mechanics: Theory and Experiment   Check publisher's open access policy
ISSN 1742-5468
Publication date 2010-01-01
Sub-type Article (original research)
DOI 10.1088/1742-5468/2010/01/P01004
Open Access Status Not Open Access
Volume 2010
Issue 1
Start page P01004-1
End page P01004-10
Total pages 10
Place of publication Bristol, United Kingdom
Publisher Institute of Physics Publishing
Language eng
Formatted abstract
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 6-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. © IOP Publishing Ltd.
Keyword Solvable lattice models
Square lattice
Q-Index Code C1
Q-Index Status Confirmed Code
Institutional Status UQ
Additional Notes Article # P01004

Document type: Journal Article
Sub-type: Article (original research)
Collections: School of Mathematics and Physics
Official 2011 Collection
Version Filter Type
Citation counts: TR Web of Science Citation Count  Cited 5 times in Thomson Reuters Web of Science Article | Citations
Scopus Citation Count Cited 2 times in Scopus Article | Citations
Google Scholar Search Google Scholar
Created: Sun, 21 Feb 2010, 10:03:07 EST