Helicity modulus and vortex density in the two-dimensional easy-plane Heisenberg model on a square lattice

We have studied the two-dimensional easy-plane Heisenberg model by using a Monte Carlo simulation. The helicity modulus and the vortex density were calculated. The Kosterlitz–Thouless transition temperature obtained from the helicity modulus was consistent with previous results obtained using different methods. The energy required to create a bound pair of vortices shows an anisotropy dependence similar to that of the Kosterlitz–Thouless transition temperature.