Several Constants Arising in Statistical Mechanics

1998/10/27 by Steven R. Finch, Finch, Steven R. · 1 citation
Mathematics · Physics and Astronomy · #05A15 #05A16 #05B50 #11Y60 #82B20 #82B41 #Combinatorics (math.CO) #FOS: Mathematics #FOS: Physical sciences #High Energy Physics - Lattice (hep-lat) #Markov Chains and Monte Carlo Methods #Mathematical Physics (math-ph) #Statistical Mechanics (cond-mat.stat-mech) #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #cond-mat.stat-mech #hep-lat #math-ph #math.CO #math.MP #msc:05A15 #msc:05A16 #msc:05B50 #msc:11Y60 #msc:82B20 #msc:82B41

paper · pdf · doi:10.48550/arxiv.math/9810155

14 pages, 5 figures, submitted to Annals of Combinatorics special issue on Statistical Mechanics and Combinatorics

openalex publication_date 1998/10/27 · arxiv created 1999/03/18 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This is a brief survey of certain constants associated with random lattice models, including self-avoiding walks, polyominoes, the Lenz-Ising model, monomers and dimers, ice models, hard squares and hexagons, and percolation models.

Citations

• Spin-spin correlation functions for the two-dimensional Ising model: Exact theory in the scaling region

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• Independent Set Enumeration and Estimation of Related Constants of Grid Graphs and Their Variants

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