Correlations for the orthogonal-unitary and symplectic-unitary transitions at the hard and soft edges

We study the lattice artefacts of the Wilson Dirac operator for QCD with two colors and fermions in the fundamental representation from the viewpoint of chiral perturbation theory. These effects are studied with the help of the following spectral observables: the level density of the Hermitian Wilson Dirac operator, the distribution of chirality over the real eigenvalues, and the chiral condensate for the quenched as well as for the unquenched theory. We provide analytical expressions for all these quantities. Moreover we derive constraints for the level density of the real eigenvalues of the non-Hermitian Wilson Dirac operator and the number of additional real modes. The latter is a good measure for the strength of lattice artefacts. All computations are confirmed by Monte Carlo simulations of the corresponding random matrix theory which agrees with chiral perturbation theory of two color QCD with Wilson fermions.

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“…the microscopic level density of continuum QCD and, thus, of chiral GOE without zero modes [65]. This approximation is shown in Figs.…”

Section: B Level Density Of D5mentioning

confidence: 93%

Dirac spectrum of the Wilson-Dirac operator for QCD with two colors

2015

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“…Based on experience with similar calculations [FNH99,FN08,FN09] we expect that this will show that to leading order the sums are Riemann sums, and so turn into integrals in the limit p → ∞.…”

Section: Bulk Scalingmentioning

confidence: 95%

A finitization of the bead process

Fleming

Forrester

Nordenstam

2010

Probab. Theory Relat. Fields

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Abstract. The bead process is the particle system defined on parallel lines, with underlying measure giving constant weight to all configurations in which particles on neighbouring lines interlace, and zero weight otherwise. Motivated by the statistical mechanical model of the tiling of an abc-hexagon by three species of rhombi, a finitized version of the bead process is defined. The corresponding joint distribution can be realized as an eigenvalue probability density function for a sequence of random matrices. The finitized bead process is determinantal, and we give the correlation kernel in terms of Jacobi polynomials. Two scaling limits are considered: a global limit in which the spacing between lines goes to zero, and a certain bulk scaling limit. In the global limit the shape of the support of the particles is determined, while in the bulk scaling limit the bead process kernel of Boutillier is reclaimed, after approriate identification of the anisotropy parameter therein.

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“…This section follows [31,33,36]; see also, [15,16]. In the unitary case (β = 2), define the trace class operator K 2 on L 2 (s, ∞) with Airy kernel K Ai (x, y) := Ai(x) Ai ′ (y) − Ai ′ (x) Ai(y)…”

Section: Summary Of Fredholm Determinant Representationsmentioning

confidence: 99%

Random Matrices, Random Processes and Integrable Systems

Harnad¹

2011

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Correlations for the orthogonal-unitary and symplectic-unitary transitions at the hard and soft edges

Cited by 120 publications

References 25 publications

Dirac spectrum of the Wilson-Dirac operator for QCD with two colors

Dirac spectrum of the Wilson-Dirac operator for QCD with two colors

A finitization of the bead process

Random Matrices, Random Processes and Integrable Systems

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