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We have performed Monte Carlo (MC) simulations on systems of L classical planar unit spins on square lattices, for L=6, 15, 30, 60, 90, and 200. The interaction between any two given spins S₁ and S₂ is given by -JS₁₂ 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 (T₂). We have found that the diffusion constant for vortex motion is given at T₂ by D0. 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 10^5 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 T₂=0. 89J/k₁, the value of =0. 50. 1, and the value of ₂=0. 240. 03, in agreement with the values predicted by the Kosterlitz-Thouless theory.
Fernández et al. (Tue,) studied this question.