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Title: Finite-temperature chiral condensate and low-lying Dirac eigenvalues in quenched SU(2) lattice gauge theory

Abstract

The spectrum of low-lying eigenvalues of the overlap Dirac operator in quenched SU(2) lattice gauge theory with tadpole-improved Symanzik action is studied at finite temperatures in the vicinity of the confinement-deconfinement phase transition defined by the expectation value of the Polyakov line. The value of the chiral condensate obtained from the Banks-Casher relation is found to drop down rapidly at T=T{sub c}, though not going to zero. At T{sub c}{sup '}{approx_equal}1.5T{sub c}{approx_equal}480 MeV the chiral condensate decreases rapidly once again and becomes either very small or zero. At T<T{sub c} the distributions of small eigenvalues are universal and are well described by the chiral orthogonal ensemble of random matrices. In the temperature range above T{sub c} where both the chiral condensate and the expectation value of the Polyakov line are nonzero the distributions of small eigenvalues are not universal. Here the eigenvalue spectrum is better described by a phenomenological model of dilute instanton-anti-instanton gas.

Authors:
 [1]; ;  [2]
  1. JIPNR, National Academy of Science, 220109 (Belarus)
  2. ITEP, 117218 Russia, Moscow, B. Cheremushkinskaya str. 25 (Russian Federation)
Publication Date:
OSTI Identifier:
21254307
Resource Type:
Journal Article
Journal Name:
Physical Review. D, Particles Fields
Additional Journal Information:
Journal Volume: 78; Journal Issue: 7; Other Information: DOI: 10.1103/PhysRevD.78.074505; (c) 2008 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 0556-2821
Country of Publication:
United States
Language:
English
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; BAG MODEL; CHIRAL SYMMETRY; CHIRALITY; CONDENSATES; CONFINEMENT; DIRAC EQUATION; DIRAC OPERATORS; DISTRIBUTION; EIGENFUNCTIONS; EIGENVALUES; GAUGE INVARIANCE; INSTANTONS; LATTICE FIELD THEORY; MEV RANGE 100-1000; PHASE TRANSFORMATIONS; RANDOMNESS; SPECTRA; SU-2 GROUPS; TEMPERATURE DEPENDENCE; TEMPERATURE RANGE

Citation Formats

Buividovich, P V, Minsk, Acad. Krasin str. 99, ITEP, 117218 Russia, Moscow, B. Cheremushkinskaya str. 25, Luschevskaya, E V, and Polikarpov, M I. Finite-temperature chiral condensate and low-lying Dirac eigenvalues in quenched SU(2) lattice gauge theory. United States: N. p., 2008. Web. doi:10.1103/PHYSREVD.78.074505.
Buividovich, P V, Minsk, Acad. Krasin str. 99, ITEP, 117218 Russia, Moscow, B. Cheremushkinskaya str. 25, Luschevskaya, E V, & Polikarpov, M I. Finite-temperature chiral condensate and low-lying Dirac eigenvalues in quenched SU(2) lattice gauge theory. United States. doi:10.1103/PHYSREVD.78.074505.
Buividovich, P V, Minsk, Acad. Krasin str. 99, ITEP, 117218 Russia, Moscow, B. Cheremushkinskaya str. 25, Luschevskaya, E V, and Polikarpov, M I. Wed . "Finite-temperature chiral condensate and low-lying Dirac eigenvalues in quenched SU(2) lattice gauge theory". United States. doi:10.1103/PHYSREVD.78.074505.
@article{osti_21254307,
title = {Finite-temperature chiral condensate and low-lying Dirac eigenvalues in quenched SU(2) lattice gauge theory},
author = {Buividovich, P V and Minsk, Acad. Krasin str. 99 and ITEP, 117218 Russia, Moscow, B. Cheremushkinskaya str. 25 and Luschevskaya, E V and Polikarpov, M I},
abstractNote = {The spectrum of low-lying eigenvalues of the overlap Dirac operator in quenched SU(2) lattice gauge theory with tadpole-improved Symanzik action is studied at finite temperatures in the vicinity of the confinement-deconfinement phase transition defined by the expectation value of the Polyakov line. The value of the chiral condensate obtained from the Banks-Casher relation is found to drop down rapidly at T=T{sub c}, though not going to zero. At T{sub c}{sup '}{approx_equal}1.5T{sub c}{approx_equal}480 MeV the chiral condensate decreases rapidly once again and becomes either very small or zero. At T<T{sub c} the distributions of small eigenvalues are universal and are well described by the chiral orthogonal ensemble of random matrices. In the temperature range above T{sub c} where both the chiral condensate and the expectation value of the Polyakov line are nonzero the distributions of small eigenvalues are not universal. Here the eigenvalue spectrum is better described by a phenomenological model of dilute instanton-anti-instanton gas.},
doi = {10.1103/PHYSREVD.78.074505},
journal = {Physical Review. D, Particles Fields},
issn = {0556-2821},
number = 7,
volume = 78,
place = {United States},
year = {2008},
month = {10}
}