  We study the problem of triviality in the four dimensional Nambu-Jona-Lasinio
model with discrete chiral symmetry using both large-N expansions and lattice
simulations. We find that logarithmic corrections to scaling appear in the
equation of state as predicted by the large-N expansion. The data from $16^4$
lattice simulations is sufficiently accurate to distinguish logarithmically
trivial scaling from power law scaling. Simulations on different lattice sizes
reveal an interesting interplay of finite size effects and triviality. We argue
that such effects are qualitatively different for theories based on fundamental
scalar rather than fermion fields. Several lessons learned here can be applied
to simulations and analyses of more challenging field theories.
