Exact replica treatment of non-Hermitean complex random matrices

Thumbnail Image

Date

Authors

Journal Title

Journal ISSN

Volume Title

Publisher

Abstract

Description

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 of non-Hermitean random matrices (GinUE). In particular, various nonperturbative fermionic replica partition functions for this random matrix model are shown to belong to a positive, semi-infinite Toda Lattice Hierarchy which, upon its Painleve reduction, yields exact expressions for the mean level density and the density-density correlation function in both bulk of the complex spectrum and near its edges. Comparison is made with an approximate treatment of non-Hermitean disordered Hamiltonians based on the "replica symmetry breaking" ansatz. A difference between our replica approach and a framework exploiting the replica limit of an infinite (supersymmetric) Toda Lattice equation is also discussed.
Dedicated to the memory of Professor Iya Ipatova; (v3: published version, references updated)

Keywords

Disordered Systems and Neural Networks, Statistical Mechanics, High Energy Physics - Theory, Mathematical Physics, Exactly Solvable and Integrable Systems

Citation

URI

http://salesiana.dossiersoluciones.com/handle/123456789/22805

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/cond-mat/0312006
 http://arxiv.org/abs/cond-mat/0312006
 Published in: Frontiers in Field Theory, edited by O. Kovras, Ch. 3, pp. 23 -- 51 (Nova Science Publishers, NY 2005). ISBN: 1-59454-127-2

Collections

arXiv