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A finite lattice identity for the honeycomb O(n) model in the presence of a boundary | | Nicholas R. Beaton
; Jan de Gier
; Anthony J. Guttmann
; | | Date: |
2 Sep 2011 | | Abstract: | Recently Duminil-Copin and Smirnov proved a long-standing conjecture of
Nienhuis, made in 1982, that the connective constant of self-avoiding walks on
the honeycomb lattice is $sqrt{2+sqrt{2}}.$ A key identity used in that proof
was later generalised by Smirnov so as to apply to a general O(n) model with
$nin [-2,2]$. We modify this model by restricting to a half-plane and
introducing a fugacity associated with surface sites, and obtain a further
generalisation of the Smirnov identity. Our identity depends naturally on the
emph{critical} surface fugacity, which for n=0 characterises the surface
adsorption transition of self-avoiding walks. | | Source: | arXiv, 1109.0358 | | Services: | Forum | Review | PDF | Favorites | |
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