Another critique of the replica trick

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.

arXiv commentLateX, 21 pages, no figures

References in corpus (4)

• Wigner-Dyson Statistics from the Replica Method
• Level Correlations in Disordered Metals: the Replica sigma-Model
• Non-perturbative results for level correlations from the replica nonlinear sigma model
• Equivariant Localization of Path Integrals

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• Structure of Lefschetz thimbles in simple fermionic systems
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• Quantum Null Energy Condition and its (non)saturation in 2d CFTs
• Optimum estimation via gradients of partition functions and information measures: a statistical-mechanical perspective
• The Distributional Zeta-Function in Disordered Field Theory
• Hilbert-space geometry of random-matrix eigenstates
• Gravity without averaging
• Exact replica treatment of non-Hermitean complex random matrices
• Directed Polymers and Interfaces in Disordered Media
• Disordered Field Theory in $d=0$ and Distributional Zeta-Function