  In this work, we investigate the consequences of the Renormalization Group
Equation (RGE) in the determination of the effective potential and the study of
Dynamical Symmetry Breaking (DSB) in an Gross-Neveu (GN) model with N fermions
fields in (1+1) dimensional space-time, which can be applied as a model to
describe certain properties of the polyacetylene. The classical Lagrangian of
the model is scale invariant, but radiative corrections to the effective
potential can lead to dimensional transmutation, when a dimensionless parameter
(coupling constant) of the classical Lagrangian is exchanged for a dimensionful
one, a dynamically generated mass for the fermion fields. For the model we are
considering, perturbative calculations of the effective potential and
renormalization group functions up to three loops are available, but we use the
RGE and the leading logs approximation to calculate an improved effective
potential, including contributions up to six loops orders. We then perform a
systematic study of the general aspects of DSB in the GN model with finite N,
comparing the results we obtain with the ones derived from the original
unimproved effective potential we started with.
