On the magnetization of two-dimensional superconductors

We calculate the magnetization of a two-dimensional superconductor in a perpendicular magnetic field near its Kosterlitz-Thouless transition and at lower temperatures. We find that the critical behavior is more complex than assumed in the literature and that, in particular, the critical magnetization is {\it not} field independent as naive scaling predicts. In the low temperature phase we find a substantial fluctuation renormalization of the mean-field result. We compare our analysis with the data on the cuprates.