Level correlations in disordered metals: The replica sigma model

We compute energy-level correlations in weakly disordered metallic grains u sing the fermionic replica method. We use the standard 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 th e correlations. We calculate the correlation functions in all three classic al ensembles Gaussian-orthogonal, -unitary, and -sympletic, including the f inite-dimensional gradient corrections. Our results coincide with those obt ained by the supersymmetric sigma model and the semiclassical trace formula . [S0163-1829(99)01230-8].