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.