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

Abstract

The Berezinskii–Kosterlitz–Thouless (BKT) transition of the two-dimensional XY 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 plausible assumptions, the associated critical temperature TBKT, H is found to be $\frac{1}{\sqrt{2}}$ exactly. Surprisingly, the value of TBKT, H obtained from our NN calculations is 0.572(3) which deviates significantly from $\frac{1}{\sqrt{2}}$. In addition, based on the helicity modulus, the TBKT, 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.