The bounded 19-vertex model

Kari Eloranta

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arXiv · 1710.03609

The bounded 19-vertex model

Kari Eloranta

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Abstract

We study the 19-vertex model of Statistical Mechanics in a square with the domain wall boundary condition. Using the minimal set of generating flip actions we build a parametrized dynamic version of the model. For all observed dynamic weight values the equilibrium states exhibit clear limit shapes. Although the model in a way incorporates the 6-vertex model, the reason for the existence of the limit shape is fundamentally more general. We conclude with a further study relating the local path geometry to the macroscopic shape geometry.

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Kari Eloranta. 2017-10-09. The bounded 19-vertex model. https://arxiv.org/abs/1710.03609

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