Berezinskii-Kosterlitz-Thouless Transition of the Two-Dimensional XY Model on the Honeycomb Lattice

The Berezinskii-Kosterlitz-Thouless (BKT) transition of the two-dimensional X Y model on the honeycomb lattice is investigated using both the techniques of Neural network (NN) and Monte Carlo simulations. It is demonstrated in the literature that, with certain plau/ sible assumptions, the associated critical temperature T-BKT,T-H is found to be 1 / root 2 exactly. Surprisingly, the value of T-BKT,T-H obtained from our NN calculations is 0.572(3), which / deviates significantly from 1 /root 2 . In addition, based on the helicity modulus, the T-BKT,T-H determined is 0.576(4), agreeing well with that resulting from the NN estimation. It will be interesting to carry out a more detailed analytic calculation to obtain a theoretical value consistent with the numerical result reached here.