  We study the restoration of spontaneously broken symmetry at nonzero
temperature in the framework of the O(2) model using polar coordinates. We
apply the CJT formalism to calculate the masses and the condensate in the
double-bubble approximation, both with and without a term that explicitly
breaks the O(2) symmetry. We find that, in the case with explicitly broken
symmetry, the mass of the angular degree of freedom becomes tachyonic above a
temperature of about 300 MeV. Taking the term that explicitly breaks the
symmetry to be infinitesimally small, we find that the Goldstone theorem is
respected below the critical temperature. However, this limit cannot be
performed for temperatures above the phase transition. We find that, no matter
whether we break the symmetry explicitly or not, there is no region of
temperature in which the radial and the angular degree of freedom become
degenerate in mass. These results hold also when the mass of the radial mode is
sent to infinity.
