  In previous studies, we proposed a scaling ansatz for electron-electron
interactions under renormalization group transformation. With the inclusion of
phonon-mediated interactions, we show that the scaling ansatz, characterized by
the divergent logarithmic length $l_d$ and a set of renormalization-group
exponents, also works rather well. The superconducting phases in a doped
two-leg ladder are studied and classified by these renormalization-group
exponents as demonstration. Finally, non-trivial constraints among the
exponents are derived and explained.
