Random matrices and the replica method

Details Random matrices and the replica method Random matrices and the replica method

1999-08-09

arxiv.org/abs/cond-mat/9908130v2

Nucl.Phys. B596 (2001) 548

Physics

Condensed Matter

Statistical Mechanics

12 pages (latex), presentation clarified, misprints fixed

Scientific paper

10.1016/S0550-3213(00)00749-5

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.

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