  We carry out a complete analytical stability study for the SO(8) symmetric
phases in the weakly-interacting two-leg ladder. It is shown that the SO(8)
symmetry is robust under generic perturbations. Since there are no fixed points
in the one-loop renormalization group equations, the conventional
classification of relevant and irrelevant perturbations fails in this case. A
new classification is defined and explained in detail. It leads to the
anomalous scaling in the ratios of excitation gaps and an universal exponent
1/3 is extracted. This new method is also applied to the well studied 2D Ising
model and similar exponent is calculated.
