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

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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