Critical behavior of the Ashkin-Teller model with a line defect: a Montecarlo study

We study magnetic critical behavior in the Ashkin-Teller model with an asymmetric defect line. This system is represented by two Ising lattices of spins $\sigma$ and $\tau$ interacting through a four-spin coupling $\epsilon$. In addition, the couplings between $\sigma$-spins are modified along a particular line, whereas couplings between $\tau$-spins are kept unaltered. This problem has been previously considered by means of analytical field-theoretical methods and by numerical techniques, with contradictory results. For $\epsilon > 0$ field-theoretical calculations give a magnetic critical exponent corresponding to $\sigma$-spins which depends on the defect strength only (it is independent of $\epsilon$), while $\tau$-spins magnetization decay with the universal Ising value $1/8$. On the contrary, numerical computations based on density matrix renormalization (DMRG) give, for $\epsilon > 0$ similar scaling behaviors for $\sigma$ and $\tau$ spins, which depend on both $\epsilon$ and defect intensity. In this paper we revisit the problem by performing a direct Montecarlo simulation. Our results are in well agreement with DMRG computations. We also discuss some possible sources for the disagreement between numerical and analytical results.