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arXiv · 2411.17497

Observation of droplets in dimer model on a triangular lattice

Daria Shvalyuk·Anton Nazarov
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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.

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Daria Shvalyuk, Anton Nazarov. 2024-11-26. Observation of droplets in dimer model on a triangular lattice. https://arxiv.org/abs/2411.17497

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