  We consider two critical semi-infinite subsystems with different critical
exponents and couple them through their surfaces. The critical behavior at the
interface, influenced by the critical fluctuations of the two subsystems, can
be quite rich. In order to examine the various possibilities, we study a system
composed of two coupled Ashkin-Teller models with different four-spin couplings
epsilon, on the two sides of the junction. By varying epsilon, some bulk and
surface critical exponents of the two subsystems are continuously modified,
which in turn changes the interface critical behavior. In particular we study
the marginal situation, for which magnetic critical exponents at the interface
vary continuously with the strength of the interaction parameter. The behavior
expected from scaling arguments is checked by DMRG calculations.
