Asymptotic Behavior of Partition Functions with Graph Laplacian

Details Asymptotic Behavior of Partition Functions with Graph Laplacian Asymptotic Behavior of Partition Functions with Graph Laplacian

2006-07-23

arxiv.org/abs/math-ph/0607050v2

Physics

Mathematical Physics

18 pages, 3 figures; misprints corrected, minor improvements of the text, one reference added

Scientific paper

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.

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