Chiral random matrix model for critical statistics

Citation
Am. Garcia-garcia et Jjm. Verbaarschot, Chiral random matrix model for critical statistics, NUCL PHYS B, 586(3), 2000, pp. 668-685
Citations number
66
Categorie Soggetti
Physics
Journal title
NUCLEAR PHYSICS B
ISSN journal
05503213 → ACNP
Volume
586
Issue
3
Year of publication
2000
Pages
668 - 685
Database
ISI
SICI code
0550-3213(20001023)586:3<668:CRMMFC>2.0.ZU;2-4
Abstract
We propose a random matrix model that interpolates between the chiral rando m matrix ensembles and the chiral Poisson ensemble. By mapping this model o n a non-interacting Fermi-gas we show that for energy differences less than a critical energy E-c the spectral correlations are given by chiral Random Matrix theory whereas for energy differences larger than E-c the number va riance shows a linear dependence on the energy difference with a slope that depends on the parameters of the model. If the parameters are scaled such that the slope remains fixed in the thermodynamic limit, this model provide s a description of QCD Dirac spectra in the universality class of critical statistics. In this way a good description of QCD Dirac spectra for gauge f ield configurations given by a liquid of instantons is obtained. (C) 2000 E lsevier Science B.V. All rights reserved.