It is shown that the phase diagram of a 2D metal undergoing a supercon
ducting transition consists of regions of a normal phase where the mod
ulus of the order parameter is absent, an ''anomalous normal'' phase w
here the modulus of the order parameter is different from zero but the
phase of the order parameter is a random quantity, and a Berezinskii-
Kosterlitz-Thouless phase. The characteristic temperatures of transiti
ons between the phases and the behavior of the chemical potential as a
function of the fermion density and temperature are found. (C) 1997 A
merican Institute of Physics.