Vertex models and random labyrinths: phase diagrams for ice-type vertex models

2004/02/25 by Kirill Shtengel, L. Chayes, L P Chayes
Materials Science · Mathematics · Physics and Astronomy · #Material Dynamics and Properties #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #cond-mat.stat-mech #cond-mat.str-el

paper · pdf · doi:10.1088/1742-5468/2005/07/p07006

published as J. Stat. Mech. (2005) P07006 · 8 pages, 6 figures

arxiv created 2004/02/25 · openalex publication_date 2005/07/27 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/30

Abstract

We propose a simple geometric recipe which allows the deduction of phase diagrams for a general class of vertex models obeying the ice rule. The disordered phase maps onto intersecting loop models which are interesting in their own right and are related to other statistical mechanical models. This mapping is also useful for the understanding of some ordered phases of these vertex models as they correspond to the polymer loop models with cross-links in their vulcanized phase.

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