Replica Field Theories, Painlevé Transcendents, and Exact Correlation Functions
Abstract
Exact solvability is claimed for nonlinear replica σ 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 Painlevé 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 classesA and AIII in Cartan classification) and Ginibre's ensemble of complex nonHermitian random matrices. Further applications are briefly discussed.
 Publication:

Physical Review Letters
 Pub Date:
 December 2002
 DOI:
 10.1103/PhysRevLett.89.250201
 arXiv:
 arXiv:condmat/0207745
 Bibcode:
 2002PhRvL..89y0201K
 Keywords:

 02.50.r;
 05.40.a;
 75.10.Nr;
 Probability theory stochastic processes and statistics;
 Fluctuation phenomena random processes noise and Brownian motion;
 Spinglass and other random models;
 Condensed Matter  Disordered Systems and Neural Networks;
 Condensed Matter  Mesoscale and Nanoscale Physics;
 High Energy Physics  Theory;
 Mathematical Physics;
 Nonlinear Sciences  Exactly Solvable and Integrable Systems
 EPrint:
 published version, 4 pages, revtex4