Level correlations in disordered metals: The replicaσmodel

We compute energy-level correlations in weakly disordered metallic grains using 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 the correlations. We calculate the correlation functions in all three classical ensembles Gaussian-orthogonal, -unitary, and -sympletic, including the finite-dimensional gradient corrections. Our results coincide with those obtained by the supersymmetric $\sigma$ model and the semiclassical trace formula.