A study of the Berezinskii-Kosterlitz-Thouless transition in the XY model in a honeycomb lattice

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.