Chiral Random Matrix Model for Critical Statistics

Details Chiral Random Matrix Model for Critical Statistics Chiral Random Matrix Model for Critical Statistics

2000-03-17

arxiv.org/abs/hep-th/0003159v2

Nucl.Phys. B586 (2000) 668-685

Physics

High Energy Physics

High Energy Physics - Theory

21 pages, 3 figures, Latex; added two references and minor corrections

Scientific paper

10.1016/S0550-3213(00)00362-X

We propose a random matrix model that interpolates between the chiral random matrix ensembles and the chiral Poisson ensemble. By mapping this model on 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 variance 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 provides 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 field configurations given by a liquid of instantons is obtained.

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