Observation of droplets in dimer model on a triangular lattice

TL;DR

This paper investigates droplet formation in a dimer model on a triangular lattice, revealing how local energies and low temperatures lead to macroscopic droplets, inspired by analogous phenomena in the Ising model.

Contribution

It demonstrates the emergence of macroscopic droplets in the dimer model, extending understanding of phase separation phenomena in lattice models.

Findings

Macroscopic droplets form at low temperatures and specific local energies.

Droplet formation is linked to superposition polygons of dimers.

Results are motivated by and connected to the Ising model behavior.

Abstract

In this paper, we consider the formation of droplets in the dimer model on a triangular lattice. The droplets in the dimer model are superposition polygons formed as two overlapping configurations of dimers: constant and movable. We demonstrate that specific local energies of dimers and low temperatures lead to the emergence of a macroscopic droplet. The motivation for this study was the phenomenon of the formation of equilibrium droplets under certain conditions in the Ising model within the framework of the Dobrushin-Koteck\'y-Shlosman theory. Due to the deep connections between the Ising model and the dimer model, similar behaviour was expected.