Edwards-Wilkinson Depinning Transition in the Background of Random Coulomb Potential

TL;DR

This study investigates the depinning transition of a 1+1 dimensional Edwards-Wilkinson interface under long-range correlated Coulomb noise, revealing a new universality class with distinct critical exponents.

Contribution

It introduces the effect of long-range correlated Coulomb noise on the EW depinning transition, identifying a new universality class with unique critical exponents.

Findings

Depinning transition occurs at critical force F_c≈0.37.

Critical exponents differ from known universality classes.

Long-range correlated noise drives the system out of EW universality.

Abstract

The Edwards-Wilkinson (EW) growth of $1+1$ interface is considered in the background of the correlated random noise. We use random Coulomb potential as the background long-range correlated noise. A depinning transition is observed in a critical driving force $F_c\approx 0.37$ in the vicinity of which the final velocity of the interface varies linearly with time. Our data collapse analysis for the velocity shows a crossover time $t^*$ at which the velocity is size independent. Based on a two-variable scaling analysis, we extract the exponents, which are different from all universality classes we are aware of. Especially noting that the dynamic and roughness exponents are $z_w=1.55\pm 0.05$, and $\alpha_w=1.05\pm 0.05$ at the criticality, we conclude that the system is different from both EW and KPZ universality classes. Our analysis shows therefore that making the noise long-range-correlated, drives the system out of EW universality class. The simulations on the tilted lattice shows that the non-linearity term ($\lambda$ term in the KPZ equations) goes to zero in the thermodynamic limit.