TY - JOUR

T1 - Observation of droplets in dimer model on a triangular lattice

AU - Назаров, Антон Андреевич

PY - 2026/1/28

Y1 - 2026/1/28

N2 - 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 have performed simulations of the system of dimers via the Monte Carlo method. 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 behavior was expected.

AB - 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 have performed simulations of the system of dimers via the Monte Carlo method. 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 behavior was expected.

KW - Dimer model

KW - Dobrushin-Kotecký-Shlosman theory

KW - Ising model

KW - Monte Carlo simulation

UR - https://www.mendeley.com/catalogue/eb4c8a55-54f8-3001-b8cd-2b28855161de/

U2 - 10.1016/j.physleta.2025.131189

DO - 10.1016/j.physleta.2025.131189

M3 - Letter

VL - 567

JO - Physics Letters A

JF - Physics Letters A

SN - 0375-9601

M1 - 131189

ER -