Study of the Nambu-Jona-Lasinio model on the lattice

We present our full analysis of the two flavor Nambu--Jona-Lasinio model with SU(2)[times]SU(2) chiral symmetry on the four-dimensional hypercubic lattice with naive and Wilson fermions. We find that this model is an excellent toy field theory to investigate issues related to lattice QCD. We use the large-[ital N] approximation to leading order in 1/[ital N] to obtain nonperturbative analytical results over almost the whole parameter range. By using numerical simulations we estimate that the size of the 1/[ital N] corrections for most of the quantities we consider are small and in this way we strengthen the validity of the leading-order large-[ital N] calculations. We obtain results regarding the approach to the continuum chiral limit, the effects of the zero momentum fermionic modes on finite lattices, and the scalar and pseudoscalar spectrum.