Effects of a local defect on one-dimensional nonlinear surface growth

TL;DR

This paper investigates the slow-bond problem in 1D KPZ surface growth, showing that the critical defect strength is zero in the thermodynamic limit, resolving a long-standing debate.

Contribution

The study uses finite-size scaling and extensive simulations to demonstrate that the nonzero critical defect strength is a crossover artifact, not a true phase transition.

Findings

Critical defect strength $oldsymbol{ eq 0}$ is a finite-size crossover effect.

Logarithmic convergence of $oldsymbol{ eq 0}$ to zero as system size increases.

Supports the hypothesis that $oldsymbol{ eq 0}$ is an artifact, not a true critical point.

Abstract

The slow-bond problem is a long-standing question about the minimal strength $\epsilon_\mathrm{c}$ of a local defect with global effects on the Kardar--Parisi--Zhang (KPZ) universality class. A consensus on the issue has been delayed due to the discrepancy between various analytical predictions claiming $\epsilon_\mathrm{c} = 0$ and numerical observations claiming $\epsilon_\mathrm{c} > 0$. We revisit the problem via finite-size scaling analyses of the slow-bond effects, which are tested for different boundary conditions through extensive Monte Carlo simulations. Our results provide evidence that the previously reported nonzero $\epsilon_\mathrm{c}$ is an artifact of a crossover phenomenon, which logarithmically converges to zero as the system size goes to infinity.