Critical resonance in the non-intersecting lattice path model

2001/11/30 by Richard Kenyon, Richard W. Kenyon, David B. Wilson · 1 citation
Mathematics · Physics and Astronomy · #Quantum chaos and dynamical systems #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #cond-mat #math.CO #math.PR #msc:60C05 #msc:82B20

paper · pdf · doi:10.1007/s00440-003-0293-z

published as Probability Theory and Related Fields 130(3):289--318, 2004 · 28 pages, 6 figures. v4 has changes suggested by referee

arxiv created 2004/06/23 · openalex publication_date 2004/08/20 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/29

Abstract

We study the phase transition in the honeycomb dimer model (equivalently, monotone non-intersecting lattice path model). At the critical point the system has a strong long-range dependence; in particular, periodic boundary conditions give rise to a ``resonance'' phenomenon, where the partition function and other properties of the system depend sensitively on the shape of the domain.

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