The large hierarchy between the gravitational and the weak force, known as the Higgs naturalness problem has been captivating physicists for decades, acting as solid guidance for model building. In the apparent absence of supersymmetry and composite dynamics at the colliders, it is tempting to associate this hierarchy with breaking scale invariance through dimensional transmutation. During my talk, I will discuss one such scenario in detail. The first part is focused on a quick review of computing quantum corrections to scalar potentials and renormalization group (RG) improvement. In the second part, I discuss the Gildener-Weinberg mechanism for breaking scale invariance and the case of multi-phase criticality wherein different phases may coexist. In the final part, I will briefly describe how formal methods of RG improvement of multiple scale effective potentials may alter the symmetry-breaking dynamics.