Abstract
We discover a hidden structure for the complex renormalization group (RG) equations of quasi-one-dimensional (Q1D) systems. It turns out that we can rewrite RG equations by the derivative of a scalar function, which is referred as RG potential. This structure provides a clear picture for the existence of fixed rays in Q1D systems. We also investigate the stability of these fixed rays and therefore introduce a new classification for the interactions under RG.