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

TL;DR

This study investigates how an asymmetric defect line affects the critical behavior of the Ashkin-Teller model, revealing different local ordering phenomena depending on the coupling strength, which challenges existing theoretical predictions.

Contribution

It provides a numerical analysis of the critical magnetization scaling at a defect line in the Ashkin-Teller model, highlighting discrepancies with recent field-theoretical results.

Findings

Identical scaling for $\sigma$ and $ au$ spins when $\e>0$

Local ordering and disordering phenomena for $\e<0$

Contradicts recent field-theoretical predictions for $\e<0$

Abstract

We consider the Ashkin-Teller model on the square lattice, which is represented by two Ising models ($\sigma$ and $\tau$) having a four-spin coupling of strength, $\epsilon$, between them. We introduce an asymmetric defect line in the system along which the couplings in the $\sigma$ 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 $\sigma$ and for $\tau$ spins by density matrix renormalization. For $\epsilon>0$ we observe identical scaling for $\sigma$ and $\tau$ spins, whereas for $\epsilon<0$ one model becomes locally ordered and the other locally disordered. This is different of the critical behavior of the uncoupled model ($\epsilon=0$) and is in contradiction with the results of recent field-theoretical calculations.