Limit shapes from harmonicity: dominos and the five vertex model

Richard Kenyon; István Prause

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arXiv · 2310.06429

Limit shapes from harmonicity: dominos and the five vertex model

Richard Kenyon·István Prause

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Abstract

We discuss how to construct limit shapes for the domino tiling model (square lattice dimer model) and $5$-vertex model, in appropriate polygonal domains. Our methods are based on the harmonic extension method of [R. Kenyon and I. Prause, Gradient variational problems in $\mathbb{R}^2$, Duke Math J. 2022].

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Richard Kenyon, István Prause. 2023-10-10. Limit shapes from harmonicity: dominos and the five vertex model. https://arxiv.org/abs/2310.06429

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