Boundary chromatic polynomial
Year: 2008
Type: preprint
Abstract: We consider proper colorings of planar graphs embedded in the annulus, such that vertices on one rim can take Q_s colors, while all remaining vertices can take Q colors. The corresponding chromatic polynomial is related to the partition function of a boundary loop model. Using results for the latter, the phase diagram of the coloring problem (with real Q and Q_s) is inferred, in the limits of two-dimensional or quasi one-dimensional infinite graphs. We find in particular that the special role played by Beraha numbers Q=4 cos^2(pi/n) for the usual chromatic polynomial does not extend to the case Q different from Q_s. The agreement with (scarce) existing numerical results is perfect; further numerical checks are presented here.
Source: arXiv (Cornell University)
Authors: Jacobsen, Jesper Lykke, Saleur, Hubert
Institution: Fédération de Recherche Interactions Fondamentales
Language: English
Subfield: Condensed Matter Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W6947895472
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