Spectral correlations of the massive QCD Dirac operator at finite temperature

Seif, Burkhard; Wettig, Tilo; Guhr, Thomas

doi:10.1016/s0550-3213(99)00130-3

Cited by 20 publications

(31 citation statements)

References 40 publications

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“…The appropriate large mass expansion for N → ∞ is described in section 6, along with the pertinent Efetov-Wegner terms for the supersymmetric limit. For a more detailed proof that the limits N → ∞ andm α → ∞ are commutable at least for the purpose of computing spectral correlation functions, see [37], where a similar supersymmetrization using fictitious supersymmetric sea quark partners was applied to the partition function of the chiral Gaussian unitary ensemble relevant for QCD 4 .…”

Section: Higher Order Spectral Correlation Functionsmentioning

confidence: 99%

Microscopic spectrum of the QCD Dirac operator in three dimensions

Szabo

2001

Nuclear Physics B

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The microscopic spectral correlators of the Dirac operator in three-dimensional Yang-Mills theory coupled to fundamental fermions and with three or more colours are derived from the supersymmetric formulation of partially quenched effective Lagrangians. The flavour supersymmetry breaking patterns are appropriately identified and used to calculate the corresponding finite volume partition functions from Itzykson-Zuber type integrals over supersymmetric cosets. New and simple determinant expressions for the spectral correlators in the mesoscopic scaling region are thereby found. The microscopic spectrum derived from the effective finite volume partition function of three-dimensional QCD agrees with earlier results based on the unitary ensemble of random matrix theory and extends the corresponding calculations for QCD in four dimensions.

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Section: Higher Order Spectral Correlation Functionsmentioning

confidence: 99%

Microscopic spectrum of the QCD Dirac operator in three dimensions

Szabo

2001

Nuclear Physics B

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“…First, the unitary invariant chRMT [2,3], corresponding to (2.1) with T = 0, in which the chiral phase transition is driven by tuning U (M 2 ). Second, the nonunitary invariant chRMT [16][17][18], corresponding to (2.1) with U (M 2 ) = M 2 , where the deterministic block matrix T mimics the effect of the temperature. In this paper we do not need to distinguish between the two approaches as they are consistent for the quantities measured here.…”

Section: Expectations From Chrmtmentioning

confidence: 99%

Microscopic universality and the chiral phase transition in two flavor QCD

et al. 2000

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We re-analyze data from available finite-temperature QCD simulations near the chiral transition, with the help of Chiral Random Matrix Theory (chRMT). Statistical properties of the lowest-lying eigenvalues of the staggered Dirac operator for SU(3) lattice gauge theory with dynamical fermions are examined. We consider temperatures below, near, and above the critical temperature Tc for the chiral phase transition. Below and above Tc the statistics are in agreement with the exact analytical predictions in the microscopic scaling regime. Above Tc we observe a gap in the spectral density and a distribution compatible with the Airy distribution. Near Tc the eigenvalue correlations appear inconsistent with chRMT.

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“…The author is most grateful to Paul Bourgade and Guillaume Dubach for generously communicating their unpublished results at an early stage which stimulated his own research on the topic. Ramis Movassagh is acknowledged for an interesting discussion and bringing reference [39] to the author's attention, Gernot Akemann for pointing out [46] and Peter Forrester for mentioning [8]. Jacek Grela and Eugene Strahov are acknowledged for their collaboration on the associated analysis of Eq.…”

Section: Introductionmentioning

confidence: 99%

On Statistics of Bi-Orthogonal Eigenvectors in Real and Complex Ginibre Ensembles: Combining Partial Schur Decomposition with Supersymmetry

Fyodorov

2018

Commun. Math. Phys.

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Abstract:We suggest a method of studying the joint probability density (JPD) of an eigenvalue and the associated 'non-orthogonality overlap factor' (also known as the 'eigenvalue condition number') of the left and right eigenvectors for non-selfadjoint Gaussian random matrices of size N × N . First we derive the general finite N expression for the JPD of a real eigenvalue λ and the associated non-orthogonality factor in the real Ginibre ensemble, and then analyze its 'bulk' and 'edge' scaling limits. The ensuing distribution is maximally heavy-tailed, so that all integer moments beyond normalization are divergent. A similar calculation for a complex eigenvalue z and the associated nonorthogonality factor in the complex Ginibre ensemble is presented as well and yields a distribution with the finite first moment. Its 'bulk' scaling limit yields a distribution whose first moment reproduces the well-known result of Chalker and Mehlig (Phys Rev Lett 81(16):3367-3370, 1998), and we provide the 'edge' scaling distribution for this case as well. Our method involves evaluating the ensemble average of products and ratios of integer and half-integer powers of characteristic polynomials for Ginibre matrices, which we perform in the framework of a supersymmetry approach. Our paper complements recent studies by Bourgade and Dubach (The distribution of overlaps between eigenvectors of Ginibre matrices, 2018. arXiv:1801.01219).

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Spectral correlations of the massive QCD Dirac operator at finite temperature

Cited by 20 publications

References 40 publications

Microscopic spectrum of the QCD Dirac operator in three dimensions

Microscopic spectrum of the QCD Dirac operator in three dimensions

Microscopic universality and the chiral phase transition in two flavor QCD

On Statistics of Bi-Orthogonal Eigenvectors in Real and Complex Ginibre Ensembles: Combining Partial Schur Decomposition with Supersymmetry

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