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Title: Chiral random matrix model at finite chemical potential: Characteristic determinant and edge universality

Authors:
; ;
Publication Date:
Sponsoring Org.:
USDOE
OSTI Identifier:
1250302
Grant/Contract Number:
FG-88ER40388; DEC-2011/02/A/ST1/00119
Resource Type:
Journal Article: Published Article
Journal Name:
Nuclear Physics. B
Additional Journal Information:
Journal Volume: 909; Journal Issue: C; Related Information: CHORUS Timestamp: 2017-05-31 10:00:34; Journal ID: ISSN 0550-3213
Publisher:
Elsevier
Country of Publication:
Netherlands
Language:
English

Citation Formats

Liu, Yizhuang, Nowak, Maciej A., and Zahed, Ismail. Chiral random matrix model at finite chemical potential: Characteristic determinant and edge universality. Netherlands: N. p., 2016. Web. doi:10.1016/j.nuclphysb.2016.04.040.
Liu, Yizhuang, Nowak, Maciej A., & Zahed, Ismail. Chiral random matrix model at finite chemical potential: Characteristic determinant and edge universality. Netherlands. doi:10.1016/j.nuclphysb.2016.04.040.
Liu, Yizhuang, Nowak, Maciej A., and Zahed, Ismail. 2016. "Chiral random matrix model at finite chemical potential: Characteristic determinant and edge universality". Netherlands. doi:10.1016/j.nuclphysb.2016.04.040.
@article{osti_1250302,
title = {Chiral random matrix model at finite chemical potential: Characteristic determinant and edge universality},
author = {Liu, Yizhuang and Nowak, Maciej A. and Zahed, Ismail},
abstractNote = {},
doi = {10.1016/j.nuclphysb.2016.04.040},
journal = {Nuclear Physics. B},
number = C,
volume = 909,
place = {Netherlands},
year = 2016,
month = 8
}

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record at 10.1016/j.nuclphysb.2016.04.040

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  • Phase diagram of a chiral random matrix model with the two degenerate quarks (u and d) and the s-quark at finite temperature and density is presented. The model exhibits a first-order transition at finite temperature for three massless flavors, owing to the U{sub A}(1) breaking determinant term. We study the order of the transition with changing the quark masses and the quark chemical potential, and show that the first-order transition region expands as the chemical potential increases. We also discuss the behavior of the meson masses and the susceptibilities near the critical point.
  • We study the effect of topology for a random matrix model of QCD at nonzero imaginary chemical potential or nonzero temperature. Nonuniversal fluctuations of Dirac eigenvalues lead to normalization factors that contribute to the {theta} dependence of the partition function. These normalization factors have to be canceled in order to reproduce the {theta} dependence of the QCD partition function. The reason for this behavior is that the topological domain of the Dirac spectrum (the region of the Dirac spectrum that is sensitive to the topological charge) extends beyond the microscopic domain at nonzero imaginary chemical potential or temperature. Such behaviormore » could persist in certain lattice formulations of QCD.« less
  • In this paper the kernel for the spectral correlation functions of invariant chiral random matrix ensembles with real ({beta}=1 ) and quaternion real ({beta}=4 ) matrix elements is expressed in terms of the kernel of the corresponding complex Hermitian random matrix ensembles ({beta}=2 ). Such identities are exact in case of a Gaussian probability distribution and, under certain smoothness assumptions, they are shown to be valid asymptotically for an arbitrary finite polynomial potential. They are proved by means of a construction proposed by Brezin and Neuberger. Universal behavior of the eigenvalues close to zero for all three chiral ensembles thenmore » follows from microscopic universality for {beta}=2 as shown by Akemann, Damgaard, Magnea, and Nishigaki. {copyright} {ital 1998} {ital The American Physical Society}« less
  • We consider two non-Gaussian ensembles of large Hermitian random matrices with strong level confinement and show that near the soft edge of the spectrum both scaled density of states and eigenvalue correlations follow so-called Airy laws inherent in the Gaussian unitary ensemble. This suggests that the invariant one-matrix models should display universal eigenvalue correlations in the soft-edge scaling limit. {copyright} {ital 1997} {ital The American Physical Society}
  • We discuss the net quark and isovector fluctuations as well as off-diagonal quark flavor susceptibilities along the chiral phase transition line in the Nambu-Jona-Lasinio (NJL) model. The model is formulated at nonzero quark and isospin chemical potentials with nonvanishing vector couplings in the isoscalar and isovector channels. We study the influence of the quark chemical potential on the quark flavor susceptibilities in detail and the dependence of the results on model parameters as well as on the quark mass. The NJL model findings are compared with recent lattice results obtained in two-flavor QCD at finite chemical potential. On a qualitativemore » level, the NJL model provides a consistent description of the dependence of quark number fluctuations on temperature and baryon chemical potential. The phase diagram and the position of the tricritical point in the NJL model are also discussed for different parameter sets.« less