  We revisit the critical behavior of classical frustrated systems using the
nonperturbative renormalization group (NPRG) equation. Our study is performed
within the local potential approximation of this equation to which is added the
flow of the field renormalization. Our flow equations are functional to avoid
possible artifacts coming from field expansions which consists in keeping only
a limited number of coupling constants. We present a simple numerical method to
follow the fixed point solution of our equations by changing gradually the
dimension d and the number N of spin-components. We explain in details the
advantage of this method as well as the numerical difficulties we encounter,
which become severe close to d = 2. The function N_c(d) separating the regions
of first and second order in the (d,N) plane is computed for d between 4 and
2.2. Our results confirm what was previously found within cruder approximation
of the NPRG equation and contradict both the fixed dimension perturbative
approach and the results obtained within the conformal bootstrap approach.
