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The three-dimensional Abelian Chern-Simons theory coupled to a scalar and afermionic field of arbitrary charge is considered in order to study conformalsymmetry breakdown and the effective potential stability. We present animproved effective potential computation based on two-loop calculations and therenormalization group equation: the later allows us to sum up series of termsin the effective potential where the power of the logarithms are one, two andthree units smaller than the total power of coupling constants (i.e., leading,next-to-leading and next-to-next-to-leading logarithms). For the sake of thiscalculation we determined the beta function of thefermion-fermion-scalar-scalar interaction and the anomalous dimension of thescalar field. We shown that the improved effective potential provides a muchmore precise determination of the properties of the theory in the broken phase,compared to the standard effective potential obtained directly from the loopcalculations. This happens because the region of the parameter space wheredynamical symmetry breaking occurs is drastically reduced by the improvementdiscussed here.

Renormalization Group and Conformal Symmetry Breaking in the Chern-Simons Theory Coupled to Matter