Critical behavior of the two-dimensionalXYmodel: A Monte Carlo simulation

We have performed Monte Carlo (MC) simulations on systems of L×{}L classical planar unit spins on square lattices, for L=6, 15, 30, 60, 90, and 200. The interaction between any two given spins S→₁ and S→₂ is given by -JS→₁{·}S→₂ if S₁ and S₂ are nearest neighbors and vanishes otherwise. In order to make sure that our results correspond to equilibrium values, we have looked into the time-dependent properties of this model in the vicinity of critical temperature (Tc). We have found that the diffusion constant for vortex motion is given at Tc by D{}0.2 (in units of nearest-neighbor distance squared per MC step per spin). The values of the relaxation times follow from the value of D. Our computer running times were typically 10⁵ MC steps per spin, larger than any relaxation time for the system sizes we deal with. We use a procedure based on finite-size scaling to establish the value of Tc=0.89J/kB, the value of {ν}=0.5±{}0.1, and the value of ηc=0.24±{}0.03, in agreement with the values predicted by the Kosterlitz-Thouless theory.