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Because of spontaneous symmetry breaking and a mass gap, Dirac spectra show universal behavior that can be understood by means of random matrix theory. We discuss the effect of a nonzero lattice spacing on QCD Dirac spectra and find tail states that have been observed before in disordered condensed matter systems. Despite the Coleman-Mermin-Wagner theorem Dirac spectra also show universal behavior in two dimensions, but the unversality classes are different from those in four dimensions and depend on the parity of the lattice. A complete classification of two dimensional lattice QCD Dirac spectra in terms of the ten fold classification of random matrix theories is given.

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Prof. Jacobus Verbaarschot, Stony Brook University
Seminarraum Theoretische Physik
Contact: not specified