PUB - Publikationen an der Universität Bielefeld

Random Matrix Theory has been successfully applied to lattice QuantumChromodynamics. In particular, a great deal of progress has been made on theunderstanding, numerically as well as analytically, of the spectral propertiesof the Wilson Dirac operator. In this paper, we study the infra-red spectrum ofthe Wilson Dirac operator via Random Matrix Theory including the three leadingorder $a^2$ correction terms that appear in the corresponding chiralLagrangian. A derivation of the joint probability density of the eigenvalues ispresented. This result is used to calculate the density of the complexeigenvalues, the density of the real eigenvalues and the distribution of thechiralities over the real eigenvalues. A detailed discussion of thesequantities shows how each low energy constant affects the spectrum. Especiallywe consider the limit of small and large (which is almost the mean field limit)lattice spacing. Comparisons with Monte Carlo simulations of the Random MatrixTheory show a perfect agreement with the analytical predictions. Furthermore wepresent some quantities which can be easily used for comparison of lattice dataand the analytical results.