Replica field theories, Painleve transcendents, and exact correlation functions

Details Replica field theories, Painleve transcendents, and exact correlation functions Replica field theories, Painleve transcendents, and exact correlation functions

2002-07-31

arxiv.org/abs/cond-mat/0207745v2

Phys.Rev.Lett. 89 (2002) 250201

Physics

Condensed Matter

Disordered Systems and Neural Networks

published version, 4 pages, revtex4

Scientific paper

10.1103/PhysRevLett.89.250201

Exact solvability is claimed for nonlinear replica sigma models derived in the context of random matrix theories. Contrary to other approaches reported in the literature, the framework outlined does not rely on traditional "replica symmetry breaking" but rests on a previously unnoticed exact relation between replica partition functions and Painleve transcendents. While expected to be applicable to matrix models of arbitrary symmetries, the method is used to treat fermionic replicas for the Gaussian unitary ensemble (GUE), chiral GUE (symmetry classes A and AIII in Cartan classification) and Ginibre's ensemble of complex non-Hermitean random matrices. Further applications are briefly discussed.

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