2002/09/30 by K. Splittorff, J. J. M. Verbaarschot · 1 citation
Chemistry · Mathematics · Physics and Astronomy · #Eigenvalues and eigenvectors #Exact solutions in general relativity #Gaussian #Lattice (music) #Limit (mathematics) #Mathematical analysis #Mathematical physics #Mathematics #Molecular spectroscopy and chirality #Physics #Quantum mechanics #Random matrix #Replica #Replica trick #Resolvent #Scaling #Scaling limit #Spectroscopy and Quantum Chemical Studies #Spin glass #Theoretical and Computational Physics #Toda lattice #Unitary state #cond-mat.dis-nn #cond-mat.stat-mech #hep-th #math-ph #math.MP
paper · pdf · doi:10.1103/physrevlett.90.041601
published as Phys.Rev.Lett. 90 (2003) 041601 · 4 pages, latex. One reference added. Discussion of GUE now in the main text. Note added. Version to appear in Phys. Rev. Lett
arxiv created 2002/12/12 · openalex publication_date 2003/01/28 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
In a recent breakthrough Kanzieper showed that it is possible to obtain exact nonperturbative random matrix results from the replica limit of the corresponding Painlevé equation. In this article we analyze the replica limit of the Toda lattice equation and obtain exact expressions for the two-point function of the Gaussian unitary ensemble and the resolvent of the chiral unitary ensemble. In the latter case both the fully quenched and the partially quenched limit are considered. This derivation explains in a natural way the appearance of both compact and noncompact integrals, the hallmark of the supersymmetric method, in the replica limit of the expression for the resolvent.