never broken in the BE limit*.

Fig. \[FIG-relative-stability\] shows a specific result for the DSM [@Quintanilla-Gyorffy-Annett-Wallington-02] that illustrates the above points. It is a phase diagram for the relative stability of ground states in which Cooper pairs have $ s $ and $ d_{x^{2}-y^{2}} $ symmetries. At weak coupling, pairing with $ l=0 $ is preferred at low and high densities, with a quantum phase transition leading to the onset of $ d_{x^{2}-y^{2}} $ pairing in the intermediate-density regime. The location of the phase boundary is accurately predicted by Eq. (\[phase transition wc\]). In contrast, as the attraction is made stronger the range of densities over which the state with $ l=2 $ is preferred becomes narrower until, above some critical value of the coupling constant, rotational symmetry is restored for all values of the density. The $ d_{x^{2}-y^{2}} $ state is thus confined to a relatively small “island” in parameter space. This result not only confirms our expectation that pairing should take place in the $ s $ state in the BE limit, but in fact suggests that $ l=0 $ is preferred at all densities, provided that the attraction is sufficiently strong. However note that the phase boundary, 