Limit shapes for the dimer model

Abstract

We prove the existence of a limit shape for the dimer model on planar periodic bipartite graphs with an arbitrary fundamental domain and arbitrary periodic weights. This proof is based on a variational principle that uses the locality of the model and the compactness of the space of states.

arXiv comment33 pages, 26 figures

References in corpus (5)

• A variational principle for domino tilings
• Stochastic six-vertex model
• Dimers on surface graphs and spin structures. II
• Planar dimers and Harnack curves
• Limit shapes and the complex burgers equation

Cited by in corpus (1)

• The domino shuffling algorithm and Anisotropic KPZ stochastic growth