Equation of state and Goldstone - mode effects 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 phase we verify the H-dependence of the magnetization M induced by Goldstone modes and determine M for V → ∞ on the coexistence line both by extrapolation and by chiral perturbation theory. This enables us to calculate the corresponding critical amplitude. At T c the critical scaling behaviour of the magnetization as a function of H is used to determine another critical amplitude. In both cases we find negative corrections-to-scaling. Our low-temperature results are well described by the perturbative form of the model's magnetic equation of state, with coefficients determined nonperturbatively from our data. The O(2) scaling function for the magnetization is found to have a smaller slope than the one for the O(4) model.