Abstract
We have generalized the network approach to include the effects of short-range imperfections in order to analyze recent experiments on mesoscopic superconducting double loops. The presence of weakly scattering imperfections causes gaps in the phase boundary $B(T)$ or $\ensuremath{\Phi}(T)$ for certain intervals of T, which depend on the magnetic flux penetrating each loop. This is accompanied by a critical temperature ${T}_{c}(\ensuremath{\Phi}),$ showing a smooth transition between symmetric and antisymmetric states. When the scattering strength of imperfections increases beyond a certain limit, gaps in the phase boundary ${T}_{c}(B)$ or ${T}_{c}(\ensuremath{\Phi})$ appear for values of magnetic flux lying in intervals around half-integer ${\ensuremath{\Phi}}_{0}=hc/2e.$ The critical temperature corresponding to these values of magnetic flux is determined mainly by imperfections in the central branch. The calculated phase boundary is in good agreement with experiment.
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