Colorings of a Hexagonal Lattice
- 1 March 1970
- journal article
- research article
- Published by AIP Publishing in Journal of Mathematical Physics
- Vol. 11 (3), 784-789
- https://doi.org/10.1063/1.1665210
Abstract
The number of ways WL of coloring the bonds of a hexagonal lattice of L sites (L large) with three colors so that no adjacent bonds are colored alike is calculated exactly, giving W = 1.20872 …. This is equivalent to counting the number of 4‐colorings of the faces of the lattice and can also be regarded as a multiple‐dimer problem. If one introduces activities corresponding to certain vertex configurations, then the system is found to have an infinite‐order phase transition between two ordered states.Keywords
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