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 Y 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.