Berezinskii-Kosterlitz-Thouless transition in the XY model on the honeycomb lattice: A comprehensive Monte Carlo analysis

Abstract: In this paper, we thoroughly examined the Berezinskii-Kosterlitz-Thouless (BKT) phase transition in the two-dimensional XY model on the honeycomb lattice. To address its thermodynamical behavior, we combined standard numerical Monte Carlo simulations with the simulated annealing (SA) protocol and entropic simulations based on the Wang-Landau (WL) algorithm. The transition temperature was determined using the second ($\Upsilon$) and fourth-order ($\Upsilon_4$) helicity modulus as the order parameter. Our best finite-size scaling analysis suggests $T_{BKT} = 0.575(8)$ from SA and $T_{BKT}=0.576(3)$ from WL. These values deviate significantly from the expected theoretical value of $1/\sqrt{2}$. We believe that this discrepancy suggests that the theoretical assumptions regarding the analytical calculation may need to be revisited. Additionally, we calculated the vortex density and the formation energy of the vortex-antivortex pairs, where the obtained vortex formation energy is $2\mu=5.80(12)$. Upon comparison with the square lattice, our results support the notion of instability of the honeycomb lattice to support the spin long-range order and give additional backing to the critical behavior we found.