Qcd, Chiral Random Matrix Theoryand Integrability

Verbaarschot, J. J. M.

doi:10.1007/1-4020-4531-x_6

Cited by 22 publications

(27 citation statements)

References 90 publications

(180 reference statements)

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“…The interested reader is referred to reviews [8,9] and the references therein. In four dimensions the Euclidean Dirac operator assumes in the chiral representation the following form…”

Section: Random Matrix Modelmentioning

confidence: 99%

Random matrix model forQCD3staggered fermions

2011

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We show that the lowest part of the eigenvalue density of the staggered fermion operator in lattice QCD3 at small lattice coupling constant β has exactly the same shape as in QCD4. This observation is quite surprising, since universal properties of the QCD3 Dirac operator are expected to be described by a non-chiral matrix model. We show that this effect is related to the specific nature of the staggered fermion discretization and that the eigenvalue density evolves towards the non-chiral random matrix prediction when β is increased and the continuum limit is approached. We propose a two-matrix model with one free parameter which interpolates between the two limits and very well mimics the pattern of evolution with β of the eigenvalue density of the staggered fermion operator in QCD3.

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“…The interested reader is referred to reviews [8,9] and the references therein. In four dimensions the Euclidean Dirac operator assumes in the chiral representation the following form…”

Section: Random Matrix Modelmentioning

confidence: 99%

Random matrix model forQCD3staggered fermions

2011

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“…The chiral or Laguerre ensemble plays a fundamental role in the low energy limit of QDC [34]. It also appears in multivariate statistics; more specifically, a chiral ensemble is equivalent to the matrix variate Wishart distribution.…”

Section: Introductionmentioning

confidence: 99%

A note on biorthogonal ensembles

Desrosiers

Forrester

2008

Journal of Approximation Theory

112

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We consider ensembles of random matrices, known as biorthogonal ensembles, whose eigenvalue probability density function can be written as a product of two determinants. These systems are closely related to multiple orthogonal functions. It is known that the eigenvalue correlation functions of such ensembles can be written as a determinant of a kernel function. We show that the kernel is itself an average of a single ratio of characteristic polynomials. In the same vein, we prove that the type I multiple polynomials can be expressed as an average of the inverse of a characteristic polynomial. We finally introduce a new biorthogonal matrix ensemble, namely the chiral unitary perturbed by a source term.Comment: 20 page

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“…There is no difference between the original theory and phase quenched theory, and both of them provide the same results. In this case, the partition function is well described as the Gaussian form of the complex matrices Φ 1,2 , which is nothing but the Ginibre ensemble [32,34].…”

Section: Discussionmentioning

confidence: 99%

Test for a universal behavior of Dirac eigenvalues in the complex Langevin method

2016

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We apply the complex Langevin (CL) method to a chiral random matrix theory (ChRMT) at non-zero chemical potential and study the nearest neighbor spacing (NNS) distribution of the Dirac eigenvalues. The NNS distribution is extracted using an unfolding procedure for the Dirac eigenvalues obtained in the CL method. For large quark mass, we find that the NNS distribution obeys the Ginibre ensemble as expected. For small quark mass, the NNS distribution follows the Wigner surmise for correct convergence case, while it follows the Ginibre ensemble for wrong convergence case. The Wigner surmise is physically reasonable from the chemical potential independence of the ChRMT. The Ginibre ensemble is known to be favored in a phase quenched QCD at finite chemical potential. Our result suggests a possibility that the originally universal behavior of the NNS distribution is preserved even in the CL method for correct convergence case.

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Qcd, Chiral Random Matrix Theoryand Integrability

Cited by 22 publications

References 90 publications

Random matrix model forQCD3staggered fermions

Random matrix model forQCD3staggered fermions

A note on biorthogonal ensembles

Test for a universal behavior of Dirac eigenvalues in the complex Langevin method

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