Corpus ID: 117090877

# Another Critique of the Replica Trick

@article{Zirnbauer1999AnotherCO,
title={Another Critique of the Replica Trick},
author={Martin R. Zirnbauer},
journal={arXiv: Mesoscale and Nanoscale Physics},
year={1999}
}
• M. Zirnbauer
• Published 22 March 1999
• Physics
• arXiv: Mesoscale and Nanoscale Physics
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… Expand
One more discussion of the replica trick: the example of the exact solution
Systematic replica field theory calculations are analysed using the examples of two particular one-dimensional ‘toy’ random models with Gaussian disorder. Due to the simplicity of the models anExpand
Disordered Dirac fermions: the marriage of three different approaches
• Physics
• 2001
Abstract We compare the critical multipoint correlation functions for two-dimensional (massless) Dirac fermions in the presence of a random su ( N ) (non-Abelian) gauge potential, obtained by threeExpand
Se p 20 09 Replica Approach in Random Matrix Theory ♯
This Chapter outlines the replica approach in Random Matrix Theory. Both fermionic and bosonic versions of the replica limit are introduced and its trickery is discussed. A brief overview of earlyExpand
Exact replica treatment of non-Hermitean complex random matrices
Recently discovered exact integrability of zero-dimensional replica field theories [E. Kanzieper, Phys. Rev. Lett. 89, 250201 (2002)] is examined in the context of Ginibre Unitary Ensemble ofExpand
Structure of Lefschetz thimbles in simple fermionic systems
• Physics
• 2014
A bstractThe Picard-Lefschetz theory offers a promising tool to solve the sign problem in QCD and other field theories with complex path-integral weight. In this paper the Lefschetz-thimble approachExpand
Universal and Nonuniversal Dynamical Conductivity in Small Metallic Grains: An Ambivalent Role of T-Invariance at Finite Frequency
The idea of random matrix theory is applicable not only to the level statistics but also to various physical observables. Taking the dynamical conductivity in isolated quantum dots with diffusiveExpand
Disordered Bose–Einstein condensate in hard walls trap
• Physics
• Journal of Physics A: Mathematical and Theoretical
• 2019
We discuss the effects of quenched disorder in a dilute Bose-Einstein condensate confined in a hard walls trap. Starting from the disordered Gross-Pitaevskii functional, we obtain a representationExpand
Conformal field theory of the integer quantum Hall plateau transition
A solution to the long-standing problem of identifying the conformal field theory governing the transition between quantized Hall plateaus of a disordered noninteracting 2d electron gas, is proposed.Expand
Hilbert Space Geometry of Random Matrix Eigenstates.
• Medicine, Physics
• Physical review letters
• 2021
The Hilbert space geometry of eigenstates of parameter-dependent random matrix ensembles is discussed, deriving the full probability distribution of the quantum geometric tensor for the Gaussian unitary ensemble and the exact joint distribution function of the Fubini-Study metric and the Berry curvature is given. Expand
Negative moments of characteristic polynomials of random matrices: Ingham–Siegel integral as an alternative to Hubbard–Stratonovich transformation
Abstract We reconsider the problem of calculating arbitrary negative integer moments of the (regularised) characteristic polynomial for N × N random matrices taken from the Gaussian Unitary EnsembleExpand

#### References

SHOWING 1-7 OF 7 REFERENCES
Wigner-Dyson Statistics from the Replica Method
• Mathematics, Physics
• 1999
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, mustExpand
LEVEL CORRELATIONS IN DISORDERED METALS : THE REPLICA SIGMA MODEL
• Physics
• 1999
We compute energy level correlations in weakly disordered metallic grains using the fermionic replica method. We use the standard sigma-model approach and show that non--trivial saddle points, whichExpand
Nonperturbative results for level correlations from the replica nonlinear σ model
• Physics
• 1999
We show that for all three standard symmetry classes (unitary, orthogonal, and symplectic), the conventional replica nonlinear $\ensuremath{\sigma}$ model gives the correct nonperturbative result forExpand
Heat Kernels and Dirac Operators
• Mathematics
• 1992
The past few years have seen the emergence of new insights into the Atiyah-Singer Index Theorem for Dirac operators. In this book, elementary proofs of this theorem, and some of its more recentExpand
Equivariant Localization of Path Integrals
We review equivariant localization techniques for the evaluation of Feynman path integrals. We develop systematic geometric methods for studying the semi-classical properties of phase space pathExpand
Differential Geometry, Lie Groups, and Symmetric Spaces
Elementary differential geometry Lie groups and Lie algebras Structure of semisimple Lie algebras Symmetric spaces Decomposition of symmetric spaces Symmetric spaces of the noncompact type SymmetricExpand