Hamiltonian Cycles on a Random Three-coordinate Lattice
Statistical Mechanics
2009-10-31 v2 High Energy Physics - Lattice
High Energy Physics - Theory
Abstract
Consider a random three-coordinate lattice of spherical topology having 2v vertices and being densely covered by a single closed, self-avoiding walk, i.e. being equipped with a Hamiltonian cycle. We determine the number of such objects as a function of v. Furthermore we express the partition function of the corresponding statistical model as an elliptic integral.
Cite
@article{arxiv.cond-mat/9801281,
title = {Hamiltonian Cycles on a Random Three-coordinate Lattice},
author = {B. Eynard and E. Guitter and C. Kristjansen},
journal= {arXiv preprint arXiv:cond-mat/9801281},
year = {2009}
}
Comments
10 pages, LaTeX, 3 eps-figures, one reference added