# Random matrix model for QCD(3) staggered fermions

Bialas P, Burda Z, Petersson B (2011)

Physical Review D 83(1).

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We show that the lowest part of the eigenvalue density of the staggered fermion operator in lattice QCD(3) at small lattice coupling constant beta has exactly the same shape as in QCD(4). This observation is quite surprising, since universal properties of the QCD(3) Dirac operator are expected to be described by a nonchiral matrix model. We show that this effect is related to the specific nature of the staggered fermion discretization and that the eigenvalue density evolves toward the nonchiral random matrix prediction when beta 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 beta of the eigenvalue density of the staggered fermion operator in QCD(3).

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Bialas P, Burda Z, Petersson B. Random matrix model for QCD(3) staggered fermions.

*Physical Review D*. 2011;83(1).Bialas, P., Burda, Z., & Petersson, B. (2011). Random matrix model for QCD(3) staggered fermions.

*Physical Review D*,*83*(1). doi:10.1103/PhysRevD.83.014507Bialas, P., Burda, Z., and Petersson, B. (2011). Random matrix model for QCD(3) staggered fermions.

*Physical Review D*83.Bialas, P., Burda, Z., & Petersson, B., 2011. Random matrix model for QCD(3) staggered fermions.

*Physical Review D*, 83(1).P. Bialas, Z. Burda, and B. Petersson, “Random matrix model for QCD(3) staggered fermions”,

*Physical Review D*, vol. 83, 2011.Bialas, P., Burda, Z., Petersson, B.: Random matrix model for QCD(3) staggered fermions. Physical Review D. 83, (2011).

Bialas, P., Burda, Z., and Petersson, Bengt. “Random matrix model for QCD(3) staggered fermions”.

*Physical Review D*83.1 (2011).
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