Physics – Condensed Matter – Disordered Systems and Neural Networks
Scientific paper
2003-11-29
Published in: Frontiers in Field Theory, edited by O. Kovras, Ch. 3, pp. 23 -- 51 (Nova Science Publishers, NY 2005). ISBN: 1-
Physics
Condensed Matter
Disordered Systems and Neural Networks
Dedicated to the memory of Professor Iya Ipatova; (v3: published version, references updated)
Scientific paper
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.
No associations
LandOfFree
Exact replica treatment of non-Hermitean complex random matrices does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Exact replica treatment of non-Hermitean complex random matrices, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Exact replica treatment of non-Hermitean complex random matrices will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-643777