Finite size scaling in the 2D XY-model and generalized universality

In recent works (BHP), a generalized universality has been proposed, linking phenomena as dissimilar as 2D magnetism and turbulence. To test these ideas, we performed a MC study of the 2D XY-model. We found that the shape of the probability distribution function for the magnetization M is non Gaussian and independent of the system size --in the range of the lattice sizes studied-- below the Kosterlitz-Thoules temperature. However, the shape of these distributions does depend on the temperature, contrarily to the BHP's claim. This behavior is successfully explained by using an extended finite-size scaling analysis and the existence of bounds for M.