Wigner-Dyson Statistics from the Replica Method

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.

13 pages, added references

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• Random Matrix Theories in Quantum Physics: Common Concepts
• On the stationary points of the TAP free energy
• An Extension of Level-spacing Universality

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