Finite-size scaling of the helicity modulus of the two-dimensional O(3) model

Using Monte Carlo methods, we compute the finite-size scaling function of the helicity modulus $\Upsilon$ of the two-dimensional O(3) model and compare it to the low temperature expansion prediction. From this, we estimate the range of validity for the leading terms of the low temperature expansion of the finite-size scaling function and for the low temperature expansion of the correlation length. Our results strongly suggest that a Kosterlitz-Thouless transition at a temperature $T > 0$ is extremely unlikely in this model.