Another Critique of the Replica Trick
نویسنده
چکیده
Kamenev and Mezard, and Yurkevich and Lerner, have recently shown how to reproduce the large-frequency asymptotics of the energy level correlations for disordered electron systems, by doing perturbation theory around the saddles of the compact nonlinear σ model derived from fermionic replicas. We present a critical review of their procedure and argue that its validity is limited to the perturbative regime of large frequency. The miraculous exactness of the saddle-point answer for β = 2 (unitary symmetry) in the universal limit, is shown to be a special feature due to the Duistermaat-Heckman theorem.
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