TY - JOUR
T1 - Crossover to non-universal microscopic spectral fluctuations in lattice gauge theory
AU - Berbenni-Bitsch, M. E.
AU - Göckeler, M.
AU - Guhr, T.
AU - Jackson, A. D.
AU - Ma, J. Z.
AU - Meyer, S.
AU - Schäfer, A.
AU - Weidenmüller, H. A.
AU - Wettig, T.
AU - Wilke, T.
N1 - Funding Information:
It is a pleasure to thank F. Karsch and J.J.M. Verbaarschot for stimulating discussions. This work was supported in part by DFG and BMBF. SM, AS and TW thank the MPI für Kernphysik, Heidelberg, for hospitality and support. The numerical simulations were performed on a CRAY T90 at the Forschungszentrum Jülich and on a CRAY T3E at the HLRS Stuttgart.
PY - 1998/10/15
Y1 - 1998/10/15
N2 - The spectrum of the Dirac operator near zero virtuality obtained in lattice gauge simulations is known to be universally described by chiral random matrix theory. We address the question of the maximum energy for which this universality persists. For this purpose, we analyze large ensembles of complete spectra of the Euclidean Dirac operator for staggered fermions. We calculate the disconnected scalar susceptibility and the microscopic number variance for the chiral symplectic ensemble of random matrices and compare the results with lattice Dirac spectra for quenched SU(2). The crossover to a non-universal regime is clearly identified and found to scale with the square of the linear lattice size and with fπ2, in agreement with theoretical expectations.
AB - The spectrum of the Dirac operator near zero virtuality obtained in lattice gauge simulations is known to be universally described by chiral random matrix theory. We address the question of the maximum energy for which this universality persists. For this purpose, we analyze large ensembles of complete spectra of the Euclidean Dirac operator for staggered fermions. We calculate the disconnected scalar susceptibility and the microscopic number variance for the chiral symplectic ensemble of random matrices and compare the results with lattice Dirac spectra for quenched SU(2). The crossover to a non-universal regime is clearly identified and found to scale with the square of the linear lattice size and with fπ2, in agreement with theoretical expectations.
KW - Chiral random matrix models
KW - Lattice simulations of QCD
KW - Scalar susceptibilty
KW - Spectrum of the Dirac operator
KW - Thouless energy
KW - Universal behaviour
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U2 - 10.1016/S0370-2693(98)01042-9
DO - 10.1016/S0370-2693(98)01042-9
M3 - Article
AN - SCOPUS:0347628226
SN - 0370-2693
VL - 438
SP - 14
EP - 20
JO - Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics
JF - Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics
IS - 1-2
ER -