Compact polymers on decorated square lattices
Statistical Mechanics
2009-10-31 v2 Soft Condensed Matter
High Energy Physics - Lattice
High Energy Physics - Theory
Abstract
A Hamiltonian cycle of a graph is a closed path that visits every vertex once and only once. It serves as a model of a compact polymer on a lattice. I study the number of Hamiltonian cycles, or equivalently the entropy of a compact polymer, on various lattices that are not homogeneous but with a sublattice structure. Estimates for the number are obtained by two methods. One is the saddle point approximation for a field theoretic representation. The other is the numerical diagonalization of the transfer matrix of a fully packed loop model in the zero fugacity limit. In the latter method, several scaling exponents are also obtained.
Cite
@article{arxiv.cond-mat/9811426,
title = {Compact polymers on decorated square lattices},
author = {Saburo Higuchi},
journal= {arXiv preprint arXiv:cond-mat/9811426},
year = {2009}
}
Comments
22pages, 6 figures, uses latex2e and graphicx. Typos corrected and the presentation improved