Publication : t98/119
Hamiltonian Cycles on Random Eulerian Triangulations
Guitter E. (CEA, DSM, SPhT (Service de Physique Théorique), F-91191 Gif-sur-Yvette, FRANCE)Kristjansen C. (The Niels Bohr Institute Blegdamsvej 17, DK-2100 Copenhagen, DENMARK)
Nielsen J.L. (The Niels Bohr Institute Blegdamsvej 17, DK-2100 Copenhagen, DENMARK)
Abstract:Année de publication : 1999
A random Eulerian triangulation is a random triangulation where an {\it even} number of triangles meet at any given vertex. We argue that the central charge increases by one if the fully packed $O(n)$ model is defined on a random Eulerian triangulation instead of an ordinary random triangulation. Considering the case $n\rightarrow 0$, this implies that the system of random Eulerian triangulations equipped with Hamiltonian cycles describes a $c=-1$ matter field coupled to 2D quantum gravity as opposed to the system of usual random triangulations equipped with Hamiltonian cycles which has $c=-2$. Hence, in this case one should see a change in the entropy exponent from the value $\gamma=-1$ to the {\it irrational} value $\gamma=\frac{-1-\sqrt{13}}{6}$ when going from a usual random triangulation to an Eulerian one. A direct enumeration of configurations confirms this change in $\gamma$.
Revue : Nucl. Phys. B [FS] 546 731-750 (1999)
DOI : 10.1016/S0550-3213(99)00058-9
Preprint : arXiv:cond-mat/9811289
PACS : 05.20.y, 04.60.Nc, 02.10.Eb
Keywords : Hamiltonian cycle, self-avoiding walk, random Eulerian
Numéro Exterieur : NBI-HE-98-28
Langue : Anglais
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