  We consider the Ashkin-Teller model on the square lattice, which is
represented by two Ising models ($\sigma$ and $\tau$) having a four-spin
coupling of strength, $\epsilon$, between them. We introduce an asymmetric
defect line in the system along which the couplings in the $\sigma$ Ising model
are modified. In the Hamiltonian version of the model we study the scaling
behavior of the critical magnetization at the defect, both for $\sigma$ and for
$\tau$ spins by density matrix renormalization. For $\epsilon>0$ we observe
identical scaling for $\sigma$ and $\tau$ spins, whereas for $\epsilon<0$ one
model becomes locally ordered and the other locally disordered. This is
different of the critical behavior of the uncoupled model ($\epsilon=0$) and is
in contradiction with the results of recent field-theoretical calculations.
