Hamiltonian Cycles on Random Eulerian Triangulations

Abstract

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.

22 pages, 9 figures, references and a comment added

References in corpus (6)

• Field theory of compact polymers on the square lattice
• An Iterative Solution of the Three-colour Problem on a Random Lattice
• Coloring Random Triangulations
• SU(N) Meander Determinants
• Hamiltonian Cycles on a Random Three-coordinate Lattice
• Counting Hamiltonian cycles on planar random lattices

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• Spanning Forests on Random Planar Lattices
• Exponents for Hamiltonian paths on random bicubic maps and KPZ
• A matrix model for strings beyond the c=1 barrier: the spin-s Heisenberg model on random surfaces
• Loop Model with Generalized Fugacity in Three Dimensions
• Hamiltonian cycles on bicolored random planar maps