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

G. DUCHOWNEY; C. NAÓN; A. IUCCI

PHYSICA A - STATISTICAL AND THEORETICAL PHYSICS

ELSEVIER SCIENCE BV

Lugar: Amsterdam; Año: 2022 vol. 597 p. 127287 - 127297

0378-4371

We study magnetic critical behavior in the two-dimensional Ashkin–Teller model withan asymmetric defect line. This system is represented by two Ising lattices of spins σand τ interacting through a four-spin coupling ε. In addition, the couplings betweenσ -spins are modified along a particular line, whereas couplings between τ -spins arekept unaltered. This problem has been previously considered by means of analyticalfield-theoretical methods and by numerical techniques, with contradictory results. Forε > 0 field-theoretical calculations give a magnetic critical exponent corresponding toσ -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, numericalcomputations based on density matrix renormalization (DMRG) give, for ε > 0 similarscaling behaviors for σ and τ spins, which depend on both ε and defect intensity. In thispaper we revisit the problem by performing a direct Monte Carlo simulation. Our resultsare in good agreement with DMRG computations. By reexamining the field-theoreticalapproach, we show how numerical and analytical results can be reconciled when a moregeneral regularization prescription is adopted.