Problems with finite density simulations of lattice QCD

Barbour, I.M.; Behilil, Nasr Eddine; Dagotto, Elbio; Karsch, Frithjof; Moreo, Adriana; Stone, Michael; Wyld, H. W.

doi:10.1016/0550-3213(86)90601-2

Cited by 179 publications

(188 citation statements)

References 23 publications

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“…Since µγ 0 is Hermitian, the Dirac operator as a whole is non-Hermitian. As a consequence, the eigenvalues are scattered in the complex plane [79]. The fermion determinant is in general complex.…”

Section: Qcd At Nonzero Chemical Potentialmentioning

confidence: 99%

Qcd, Chiral Random Matrix Theoryand Integrability

Verbaarschot

2006

NATO Science Series II: Mathematics, Physics and Chemistry

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SummaryRandom Matrix Theory has been a unifying approach in physics and mathematics. In these lectures we discuss applications of Random Matrix Theory to QCD and emphasize underlying integrable structures. In the first lecture we give an overview of QCD, its low-energy limit and the microscopic limit of the Dirac spectrum which, as we will see in the second lecture, can be described by chiral Random Matrix Theory. The main topic of the third lecture is the recent developments on the relation between the QCD partition function and integrable hierarchies (in our case the Toda lattice hierarchy). This is an efficient way to obtain the QCD Dirac spectrum from the low energy limit of the QCD partition function. Finally, we will discuss the QCD Dirac spectrum at nonzero chemical potential. We will show that the microscopic spectral density is given by the replica limit of the Toda lattice equation. Recent results by Osborn on the Dirac spectrum of full QCD will be discussed.

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Section: Qcd At Nonzero Chemical Potentialmentioning

confidence: 99%

Qcd, Chiral Random Matrix Theoryand Integrability

Verbaarschot

2006

NATO Science Series II: Mathematics, Physics and Chemistry

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“…The eigenvalues form a connected droplet in the z-plane for µ < µ c , and split to 2 symmetric droplets for µ > µ c restoring chiral symmetry [9,10]. Similar droplets follow from the QCD Dirac spectra at finite µ on the lattice [15]. In the spontaneously broken phase, all droplets are connected and symmetric about the real-axis…”

Section: The Modelmentioning

confidence: 81%

“…Specifically, at finite µ the Dirac spectrum on the lattice is complex [15]. The matrix models at finite µ [9,11] capture this essential aspect of the lattice spectra and the nature of the chiral phase transition [1,13,14].…”

Section: The Modelmentioning

confidence: 99%

Hydrodynamical description of the QCD Dirac spectrum at finite chemical potential

2015

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We present a hydrodynamical description of the QCD Dirac spectrum at finite chemical potential as an uncompressible droplet in the complex eigenvalue space. For a large droplet, the fluctuation spectrum around the hydrostatic solution is gapped by a longitudinal Coulomb plasmon, and exhibits a frictionless odd viscosity. The stochastic relaxation time for the restoration/breaking of chiral symmetry is set by twice the plasmon frequency. The leading droplet size correction to the relaxation time is fixed by a universal odd viscosity to density ratio ηO/ρ0 = (β − 2)/4 for the three Dyson ensembles β = 1, 2, 4.

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“…The free energy density defined through the average of the modulus differs from the complete one by means of the phase contribution (1). With N independent configurations the best we can do is to evaluate e iφ ∆ with an error of the order of O( 1 √ N ).…”

Section: Strong Coupling Resultsmentioning

confidence: 99%

“…mean field). In this limit they predict a strong first order saturation transition at a value for the chemical potential significantly smaller than one third of the baryon mass [1] (as one could naively expect considering the quarks confined inside hadrons but ignoring their binding energy). The inclusion of some β dependence in analytical calculations indicates that the mean field critical density and 1 3 m B converge toward a common limit in the physically relevant scaling region [2].…”

Section: Introductionmentioning

confidence: 99%

Phase transition(s) in finite density QCD

Aloisio¹,

Azcoiti²,

Carlo³

et al. 1998

Nuclear Physics A

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The Grand Canonical formalism is generally used in numerical simulations of finite density QCD since it allows free mobility in the chemical potential µ. We show that special care has to be used in extracting numerical results to avoid dramatic rounding effects and spurious transition signals. If we analyze data correctly, with reasonable statistics, no signal of first order phase transition is present and results using the Glasgow prescription are practically coincident with the ones obtained using the modulus of the fermionic determinant.

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Problems with finite density simulations of lattice QCD

Cited by 179 publications

References 23 publications

Qcd, Chiral Random Matrix Theoryand Integrability

Qcd, Chiral Random Matrix Theoryand Integrability

Hydrodynamical description of the QCD Dirac spectrum at finite chemical potential

Phase transition(s) in finite density QCD

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