Level Correlations In Disordered Metals: The Replica Sigma Model

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. [S0163-1829(99)01230-8].