Replica Field Theories, Painlevé Transcendents, and Exact Correlation Functions
Replica Field Theories, Painlevé Transcendents, and Exact Correlation Functions
Exact solvability is claimed for nonlinear replica $\ensuremath{\sigma}$ 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 Painlev\'e …