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Level correlations in disordered metals: The replica<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>σ</mml:mi></mml:math>model
We compute energy-level correlations in weakly disordered metallic grains using the fermionic replica method. We use the standard $\ensuremath{\sigma}$-model approach and show that nontrivial saddle points, which break replica symmetry, must be included in the calculation to reproduce the oscillatory behavior of the correlations. We calculate the correlation functions in …