  Motivated by the statistical fluctuation of Dirac spectrum of QCD-like
theories subjected to (pseudo)reality-violating perturbations and in the
epsilon-regime, we compute the smallest eigenvalue distribution and the level
spacing distribution of chiral and non-chiral parametric random matrix
ensembles of Dyson-Mehta-Pandey type. To this end we employ the Nystrom method
to numerically evaluate the Fredholm Pfaffian of the integral kernel for the
chG(O,S)E-chGUE and G(O,S)E-GUE crossover. We confirm the validity and
universality of our results by comparing them with several lattice models,
namely fundamental and adjoint staggered Dirac spectra of SU(2) quenched
lattice gauge theory under the twisted boundary condition (imaginary chemical
potential) or perturbed by phase noise. Both in the zero-virtuality region and
in the spectral bulk, excellent one-parameter fitting is achieved already on a
small 4^4 lattice. Anticipated scaling of the fitting parameter with the
twisting phase, mean level spacing, and the system size allows for precise
determination of the pion decay (diffusion) constant F in the low-energy
effective Lagrangian.
