Wigner-Dyson Statistics from the Replica Method

Alex Kamenev, Marc Mezard

Published 1999-01-12, updated 1999-03-09Version 2

We compute the correlation functions of the eigenvalues in the Gaussian unitary ensemble using the fermionic replica method. We show that non--trivial saddle points, which break replica symmetry, must be included in the calculation in order to reproduce correctly the exact results for the correlation functions at large distance.