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Tue, 03 Jul 2001 00:00:00 +0200Tue, 03 Jul 2001 00:00:00 +0200Random Matrix Theory, Chiral Perturbation Theory, and Lattice Data
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1310
Abstract: Recently, the chiral logarithms predicted by quenched chiral perturbation theory have been extracted from lattice calculations of hadron masses. We argue that the deviations of lattice results from random matrix theory starting around the so-called Thouless energy can be understood in terms of chiral perturbation theory as well. Comparison of lattice data with chiral perturbation theory formulae allows us to compute the pion decay constant. We present results from a calculation for quenched SU(2) with Kogut-Susskind fermions at ß = 2.0 and 2.2.M. E. Berbenni-Bitsch; M. Göckeler; H. Hehl; S. Meyer; P.E.L. Rakow; A. Schäfer; T. Wettigpreprinthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1310Tue, 03 Jul 2001 00:00:00 +0200Random Matrix Theory and Chiral Logarithms
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1311
Abstract: Recently, the contributions of chiral logarithms predicted by quenched chiral perturbation theory have been extracted from lattice calculations of hadron masses. We argue that a detailed comparison of random matrix theory and lattice calculations allows for a precise determination of such corrections. We estimate the relative size of the m log(m), m, and m^2 corrections to the chiral condensate for quenched SU(2).M. E. Berbenni-Bitsch; M. Göckeler; H. Hehl; S. Meyer; P.E.L. Rakow; A. Schäfer; T. Wettigpreprinthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1311Tue, 03 Jul 2001 00:00:00 +0200Beyond the Thouless energy
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1309
Abstract: The distribution and the correlations of the small eigenvalues of the Dirac operator are described by random matrix theory (RMT) up to the Thouless energy E_= 1 / sqrt (V), where V is the physical volume. For somewhat larger energies, the same quantities can be described by chiral perturbation theory (chPT). For most quantities there is an intermediate energy regime, roughly 1/V < E < 1/sqrt (V), where the results of RMT and chPT agree with each other. We test these predictions by constructing the connected and disconnected scalar susceptibilities from Dirac spectra obtained in quenched SU(2) and SU(3) simulations with staggered fermions for a variety of lattice sizes and coupling constants. In deriving the predictions of chPT, it is important totake into account only those symmetries which are exactly realized on the lattice.M. E. Berbenni-Bitsch; M. Göckeler; H. Hehl; S. Meyer; P.E.L. Rakow; A. Schäfer; T. Wettigpreprinthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1309Tue, 03 Jul 2001 00:00:00 +0200Universal and non-universal behavior in Dirac spectra
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/881
We have computed ensembles of complete spectra of the staggered Dirac operator using four-dimensional SU(2) gauge fields, both in the quenched approximation and with dynamical fermions. To identify universal features in the Dirac spectrum, we compare the lattice data with predictions from chiral random matrix theory for the distribution of the low-lying eigenvalues. Good agreement is found up to some limiting energy, the so-called Thouless energy, above which random matrix theory no longer applies. We determine the dependence of the Thouless energy on the simulation parameters using the scalar susceptibility and the number variance.M. E. Berbenni-Bitsch; M. Göckeler; S. Meyer; A. Schäfer; J. J. M. Verbaarschot; T. Wettigpreprinthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/881Mon, 03 Apr 2000 00:00:00 +0200