Hamiltonian Cycles on Random Eulerian Triangulations

Details Hamiltonian Cycles on Random Eulerian Triangulations Hamiltonian Cycles on Random Eulerian Triangulations

1998-11-19

arxiv.org/abs/cond-mat/9811289v2

Nucl.Phys. B546 (1999) 731

Physics

Condensed Matter

Statistical Mechanics

22 pages, 9 figures, references and a comment added

Scientific paper

10.1016/S0550-3213(99)00058-9

A random Eulerian triangulation is a random triangulation where an 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 -> 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 irrational value gamma=(-1-\sqrt{13})/6=-0.76759... when going from a usual random triangulation to an Eulerian one. A direct enumeration of configurations confirms this change in gamma.

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