  Renormalization group theory allows continuous variation of critical
exponents along a marginal direction (when there is one), keeping the scaling
relations invariant. We propose a super universality hypothesis (SUH)
suggesting that, up to constant scale factors, the scaling functions along the
critical line must be identical to that of the base universality class even
when all the critical exponents vary continuously. We demonstrate this in the
Ashkin Teller (AT) model on a two-dimensional square lattice where two
different phase transitions occur across the self-dual critical line: while
magnetic transition obeys the weak-universality hypothesis where exponent
ratios remain fixed, the polarization exhibits a continuous variation of all
critical exponents. The SUH not only explains both kinds of variations observed
in the AT model, it also provides a unified picture of continuous variation of
critical exponents observed in several other contexts.
