Exact replica treatment of non-Hermitean complex random matrices

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dc.creatorKanzieper, Eugene
dc.date2003-11-29
dc.date2005-03-05
dc.date.accessioned2026-07-07T02:55:03Z
dc.date.available2026-07-07T02:55:03Z
dc.descriptionRecently 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.
dc.descriptionDedicated to the memory of Professor Iya Ipatova; (v3: published version, references updated)
dc.identifierhttps://arxiv.org/abs/cond-mat/0312006
dc.identifierhttp://arxiv.org/abs/cond-mat/0312006
dc.identifierPublished in: Frontiers in Field Theory, edited by O. Kovras, Ch. 3, pp. 23 -- 51 (Nova Science Publishers, NY 2005). ISBN: 1-59454-127-2
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/22805
dc.subjectDisordered Systems and Neural Networks
dc.subjectStatistical Mechanics
dc.subjectHigh Energy Physics - Theory
dc.subjectMathematical Physics
dc.subjectExactly Solvable and Integrable Systems
dc.titleExact replica treatment of non-Hermitean complex random matrices
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