Berezinskii-Kosterlitz-Thouless phase transition for the dilute planar rotator model on a triangular lattice

The Berezinskii-Kosterlitz-Thouless (BKT) phase transition for the dilute planar rotator model on a triangular lattice is studied by using a hybrid Monte Carlo method. The phase-transition temperatures for different nonmagnetic impurity densities are obtained by three approaches: finite-size scaling of plane magnetic susceptibility, helicity modulus, and Binder’s fourth cumulant. It is found that the phase-transition temperature decreases with increasing impurity density $\rho$ and the BKT phase transition vanishes when the magnetic occupancy falls to the site percolation threshold: $1-{\rho }_c=p_c=0.5$.

Figure 1

Application of Binder’s fourth order cumulant to estimate the phase-transition temperature for several lattice sizes at $\rho =0.05$. The inset shows the view near the estimated critical temperature.

Figure 2

Application of the finite-size scaling of in-plane susceptibility to estimate the phase-transition temperature for $\rho =0.05$.

Figure 3

Helicity modulus as a function of temperature for several lattice sizes at $\rho =0.05$. The inset shows the view near the estimated critical temperature.

Figure 4

Helicity modulus as a function of temperature for lattice size $L=80$ at different nonmagnetic impurity densities $\rho$. The overall trend and the results near the percolation threshold are shown in (a) and (b) separately.

Figure 5

Application of the finite-size scaling of in-plane susceptibility to estimate the phase-transition temperature for $\rho =0.45$.

Figure 6

Phase-transition temperature estimated by the three methods for different nonmagnetic impurity densities $\rho$. The straight line is a linear fit to $T_C$ obtained from the helicity modulus.