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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 $σ$ and $τ$ interacting through a four-spin coupling $ε$. In addition, the couplings between $σ$-spins are modified along a particular line, whereas couplings between $τ$-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 $ε> 0$ field-theoretical calculations give a magnetic critical exponent corresponding to $σ$-spins which depends on the defect strength only (it is independent of $ε$), while $τ$-spins magnetization decay with the universal Ising value $1/8$. On the contrary, numerical computations based on density matrix renormalization (DMRG) give, for $ε> 0$ similar scaling behaviors for $σ$ and $τ$ spins, which depend on both $ε$ 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.