  We continue the investigation on the applications of the Kramers equation to
the numerical simulation of field theoretic models. In a previous paper we have
described the theory and proposed various algorithms. Here, we compare the
simplest of them with the Hybrid Monte Carlo algorithm studying the
two-dimensional lattice Gross-Neveu model. We used a Symanzik improved action
with dynamical Wilson fermions. Both the algorithms allow for the determination
of the critical mass. Their performances in the definite phase simulations are
comparable with the Hybrid Monte Carlo. For the two methods, the numerical
values of the measured quantities agree within the errors and are compatible
with the theoretical predictions; moreover, the Kramers algorithm is safer from
the point of view of the numerical precision.
