Asymptotic Behavior of Partition Functions with Graph Laplacian
Mathematical Physics
2007-05-23 v2 Combinatorics
math.MP
Abstract
We introduce the matrix sums that represent a discrete analog of the matrix models with quartic potential. The probability space is given by the set of all simple n-vertex graphs with the Gibbs weight determined by the graph Laplacian. We study the large-n limit of the free energy per site and show that it is determined by the number of connected acyclic diagrams on the set of two-valent vertices.
Keywords
Cite
@article{arxiv.math-ph/0607050,
title = {Asymptotic Behavior of Partition Functions with Graph Laplacian},
author = {Oleksiy Khorunzhiy},
journal= {arXiv preprint arXiv:math-ph/0607050},
year = {2007}
}
Comments
18 pages, 3 figures; misprints corrected, minor improvements of the text, one reference added