Limit shapes for the dimer model

TL;DR

This paper establishes the existence of a limit shape for the dimer model on planar bipartite graphs with periodic weights, using a variational principle based on locality and compactness.

Contribution

It provides a general proof of limit shape existence for the dimer model on arbitrary periodic bipartite graphs, extending previous results to more general settings.

Findings

Proves the existence of a limit shape for the dimer model.

Uses a variational principle based on locality and compactness.

Applies to graphs with arbitrary fundamental domains and weights.

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.