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

TL;DR

This study uses Monte Carlo simulations to analyze the critical behavior of the Ashkin-Teller model with a line defect, clarifying discrepancies between previous analytical and numerical results.

Contribution

It provides a direct Monte Carlo analysis that confirms DMRG findings and discusses reasons for disagreements with analytical predictions.

Findings

Monte Carlo results agree with DMRG computations.

Critical exponents depend on both defect strength and coupling parameter.

Discrepancies with analytical methods are discussed.

Abstract

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.