The Influence of Boundary Conditions in the Six-Vertex Model

2002/05/09 by Paul Zinn-Justin, P. Zinn-Justin, Zinn-Justin, P.
Computer Science · Mathematics · Physics and Astronomy · #FOS: Physical sciences #Random Matrices and Applications #Statistical Mechanics (cond-mat.stat-mech) #Theoretical and Computational Physics #Topological and Geometric Data Analysis #cond-mat.stat-mech

paper · pdf · doi:10.48550/arxiv.cond-mat/0205192

arxiv created 2002/05/09 · openalex publication_date 2002/05/09 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We discuss the influence of boundary conditions on the continuum limit of the six-vertex model by deriving a variational principle for the associated height function with arbitrary fixed boundary conditions. We discuss its consequences using the known phase diagram of the six-vertex model. In some particular cases we compute explicitly the corresponding partial differential equations by means of the Bethe Ansatz.

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