A 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 $N$ approximation to leading order in $1/N$ to obtain non perturbative analytical results over almost the whole parameter range. By using numerical simulations we estimate that the size of the $1/N$ corrections for most of the quantities we consider are small and in this way we strengthen the validity of the leading order large $N$ 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. Note: The full ps file of this preprint is also available via anonymous ftp to ftp.scri.fsu.edu. To get the ps file, ftp to this address and use for username "anonymous" and for password your complete E-mail address. The file is in the directory pub/vranas (to go to that directory type: cd pub/vranas) and is called NJL_long.ps (to get it type: get NJL_long.ps)