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

Abstract

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, ǫ, 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 ǫ > 0 we observe identical scaling for σ and τ spins, whereas for ǫ < 0 one model becomes locally ordered and the other locally disordered. This is different of the critical behavior of the uncoupled model (ǫ = 0) and is in contradiction with the results of recent field-theoretical calculations.