  We studied the correlated quasi-one-dimensional systems by one-loop
renormalization group techniques in weak coupling. In contrast to conventional
g-ology approach, we formulate the theory in terms of bilinear currents and
obtain all possible interaction vertices. Furthermore, the one-loop
renormalization group equations are derived by operator product expansions of
these currents at short length scale. It is rather remarkable that these
coupled non-linear equations, after appropriate rescaling, can be casted into
potential flows. The existence of what we nicknamed "RG potential" provides a
natural explanation of the emergent symmetry enhancement in ladder systems.
Further implications arisen from the RG potential are also discussed at the
end.
