For the weakly coupled lattice %6 theory in a hierarchical model approximation a nonperturbative renormalization group analysis in the spirit of Gawadzki and Kupiainen is performed to study the flow of the effective actions. We deduce a domain of attraction to the tricritical (Gaussian) fixed point. The two relevant coupling constants of the problem are controlled by analytic continuation to complex domains, tracing their images under the renormalization group iterations.