  We consider the critical behavior at an interface which separates two
semi-infinite subsystems belonging to different universality classes, thus
having different set of critical exponents, but having a common transition
temperature. We solve this problem analytically in the frame of mean-field
theory, which is then generalized using phenomenological scaling
considerations. A large variety of interface critical behavior is obtained
which is checked numerically on the example of two-dimensional q-state Potts
models with q=2 to 4. Weak interface couplings are generally irrelevant,
resulting in the same critical behavior at the interface as for a free surface.
With strong interface couplings, the interface remains ordered at the bulk
transition temperature. More interesting is the intermediate situation, the
special interface transition, when the critical behavior at the interface
involves new critical exponents, which however can be expressed in terms of the
bulk and surface exponents of the two subsystems. We discuss also the smooth or
discontinuous nature of the order parameter profile.
