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Wigner-Dyson Statistics from the Replica Method

Alex Kamenev·Marc Mezard
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Abstract

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.

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Alex Kamenev, Marc Mezard. 1999-03-09. Wigner-Dyson Statistics from the Replica Method. https://doi.org/10.1088/0305-4470%2F32%2F24%2F304

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