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Another critique of the replica trick

Martin R. Zirnbauer
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Abstract

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 sigma 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 beta = 2 (unitary symmetry) in the universal limit, is shown to be a special feature due to the Duistermaat-Heckman theorem.

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Martin R. Zirnbauer. 1999-03-22. Another critique of the replica trick. https://arxiv.org/abs/cond-mat/9903338

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