Random matrices and the replica method

Abstract

Recent developments [Kamenev and Mezard, cond-mat/9901110, cond-mat/9903001; Yurkevich and Lerner, cond-mat/9903025; Zirnbauer, cond-mat/9903338] have revived a discussion about applicability of the replica approach to description of spectral fluctuations in the context of random matrix theory and beyond. The present paper, concentrating on invariant non-Gaussian random matrix ensembles with orthogonal, unitary and symplectic symmetries, aims to demonstrate that both the bosonic and the fermionic replicas are capable of reproducing nonperturbative fluctuation formulas for spectral correlation functions in entire energy scale, including the self-correlation of energy levels, provided no sigma-model mapping is used.

12 pages (latex), presentation clarified, misprints fixed

References in corpus (8)

• Correlation Functions, Cluster Functions and Spacing Distributions for Random Matrices
• Wigner-Dyson Statistics from the Replica Method
• Universality in Chiral Random Matrix Theory at $\beta =1$ and $\beta =4$
• Level Correlations in Disordered Metals: the Replica sigma-Model
• Non-perturbative results for level correlations from the replica nonlinear sigma model
• Two-band random matrices
• Random matrix models with log-singular level confinement: method of fictitious fermions
• Novel universal correlations in invariant random-matrix models

Cited by in corpus (8)

• Factorization of Correlation Functions and the Replica Limit of the Toda Lattice Equation
• Negative moments of characteristic polynomials of random matrices: Ingham-Siegel integral as an alternative to Hubbard-Stratonovich transformation
• Replica Limit of the Toda Lattice Equation
• Replica field theories, Painleve transcendents, and exact correlation functions
• Eigenvalue correlations in non-Hermitean symplectic random matrices
• Equivalence of replica and cavity methods for computing spectra of sparse random matrices
• Typical kernel size and number of sparse random matrices over GF(q) - a statistical physics approach
• The gradient flow of the Dirac spectrum