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Numerical study of the critical behavior of the Ashkin-Teller model at a line defect

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