Critical behavior of the Ashkin–Teller model with a line defect: Towards reconciliation between numerical and analytical results

Abstract

We study magnetic critical behavior in the two-dimensional 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 Monte Carlo simulation. Our results are in good agreement with DMRG computations. By reexamining the field-theoretical approach, we show how numerical and analytical results can be reconciled when a more general regularization prescription is adopted.