  In systems displaying a bulk first-order transition the order parameter may
vanish continuously at a free surface, a phenomenon which is called
surface-induced disorder. In the presence of surface-induced disorder the
correlation lengths, parallel and perpendicular to the surface, diverge at the
bulk transition point. In this way the surface induces an anisotropic power-law
singular behavior for some bulk quantities. For example in a finite system of
transverse linear size L, the response functions diverge as L^{(d-1)z+1}, where
d is the dimension of the system and z is the anisotropy exponent. We present a
general scaling picture for this anisotropic discontinuity fixed point. Our
phenomenological results are confronted with analytical and numerical
calculations on the 2D q-state Potts model in the large-q limit. The scaling
results are demonstrated to apply also for the same model with a layered,
Fibonacci-type modulation of the couplings for which the anisotropy exponent is
a continuous function of the strength of the quasiperiodic perturbation.
