A numerical study of Goldstone-mode effects and scaling functions of the three-dimensional O(2) model

We investigate numerically the three-dimensional O(2) model on 8(3) - 160(3 ) lattices as a function of the magnetic field H. In the low-temperature ph ase we verify the H-dependence of the magnetization hi induced by the Golds tone modes and determine M in the thermodynamic limit on the coexistence li ne both by extrapolation and by chiral perturbation theory. We compute two critical amplitudes from the scaling behaviours on the coexistence line and on the critical line. In both cases we find negative corrections to scalin g. With additional high temperature data we calculate the scaling function and show that it has a smaller slope than that of the O(4) model. For futur e tests of QCD lattice data we study as well finite-size-scaling functions.