  In this study, we examined the Berezinskii-Kosterlitz-Thouless (BKT) phase
transition in the two-dimensional XY model on a honeycomb lattice. The XY model
consists of normalized vectors arranged in a plane and is used to represent
two-dimensional magnetic systems. It has applications in areas such as
spintronics, superconductivity, and topological quantum computing. To calculate
the thermodynamic properties of the system, we used numerical Monte Carlo
simulations with the Metropolis algorithm and the Simulated Annealing protocol.
The transition temperature was calculated using the second and fourth-order
helicity modulus as the order parameter. We also calculated the vortex density
and the formation energy of vortex-antivortex pairs. Our findings suggest that
the critical temperature is $T_{BKT} = 0.576 \pm 0.001$, and the vortex
formation energy is $2\mu=4.0 \pm 0.5$. When compared to the square lattice,
both results support the notion of the honeycomb lattice's instability.
