Crossover and scaling in a two-dimensional field-tuned superconductor

Using an analysis similar to that of Imry and Wortis, it is shown that the apparent first-order superconductor to metal transition, which has been claimed to exist at low values of the magnetic field in a two-dimensional field-tuned system at zero temperature, can be consistently interpreted as a sharp crossover from a strong superconductor to an inhomogeneous state, which is a weak superconductor. The true zero-temperature superconductor to insulator transition within the inhomogeneous state is conjectured to be that of randomly diluted XY model. An explanation of the observed finite-temperature approximate scaling of resistivity close to the critical point is speculated within this model.