Observation of droplets in dimer model on a triangular lattice

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-Kotecký-Shlosman theory. Due to the deep connections between the Ising model and the dimer model, similar behaviour was expected.

9 pages, 5 figures