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HAIT Journal of Science and Engineering Volume 1, Issue 1, pp. 101-129 © 2004 Holon Academic Institute of Technology | ||||||
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On exact integrability of replica field theories in 0 dimensions: | ||||||
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Department of Sciences, Holon Academic Institute of Technology, Holon 58102, Israel e-mail: eugene.kanzieper@weizmann.ac.il Received 19 December 2003 | ||||||
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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 fermi-onic replica partition functions for this random matrix model are shown to belong to a positive, semi-infinite Toda Lattice Hierarchy which, upon its Painlevé 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. | ||||||
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___________________ Presented at Russian-Israeli Conference Frontiers in Condensed Matter Physics Shoresh, Israel, 19-24 October 2003 |