Asymptotic Behavior of Partition Functions with Graph Laplacian

2006/07/23 by Oleksiy Khorunzhiy, Khorunzhiy, Oleksiy
Computer Science · Mathematics · #05C80 #15A52 #60F99 #Advanced Graph Theory Research #Combinatorics (math.CO) #FOS: Mathematics #FOS: Physical sciences #Graph theory and applications #Limits and Structures in Graph Theory #Mathematical Physics (math-ph)

paper · pdf · doi:10.48550/arxiv.math-ph/0607050

openalex publication_date 2006/07/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

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