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We propose a simple geometric recipe for constructing phase diagrams for ageneral class of vertex models obeying the ice rule. The disordered phase mapsonto the intersecting loop model which is interesting in its own right and isrelated to several other statistical mechanical models. This mapping is alsouseful in understanding some ordered phases of these vertex models as theycorrespond to the polymer loop models with cross-links in their vulcanisedphase.Comment: 8 pages, 6 figure

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