1110.2690 (Mario Kieburg et al.)

Random Matrix Models for Dirac Operators at finite Lattice Spacing    [PDF]

Mario Kieburg, Jacobus J. M. Verbaarschot, Savvas Zafeiropoulos

We study discretization effects of the Wilson and staggered Dirac operator
with $N_{\rm c}>2$ using chiral random matrix theory (chRMT). We obtain
analytical results for the joint probability density of Wilson-chRMT in terms
of a determinantal expression over complex pairs of eigenvalues, and real
eigenvalues corresponding to eigenvectors of positive or negative chirality as
well as for the eigenvalue densities. The explicit dependence on the lattice
spacing can be readily read off from our results which are compared to
numerical simulations of Wilson-chRMT. For the staggered Dirac operator we have
studied random matrices modeling the transition from non-degenerate eigenvalues
at non-zero lattice spacing to degenerate ones in the continuum limit.

View original: http://arxiv.org/abs/1110.2690