Critical exponents of the driven elastic string in a disordered medium

TL;DR

This paper investigates the critical behavior of a driven elastic string in a disordered medium, calculating key exponents and observing a crossover in roughness, providing insights into depinning phenomena.

Contribution

It provides new precise measurements of critical exponents and reveals a crossover in the roughness exponent, enhancing understanding of elastic string depinning.

Findings

Velocity exponent beta = 0.33(2)

Roughness exponent zeta crosses from 1.26 to 0.5

Correlation length exponent nu = 1.29(5)

Abstract

We analyze the harmonic elastic string driven through a continuous random potential above the depinning threshold. The velocity exponent beta = 0.33(2) is calculated. We observe a crossover in the roughness exponent zeta from the critical value 1.26 to the asymptotic (large force) value of 0.5. We calculate directly the velocity correlation function and the corresponding correlation length exponent nu = 1.29(5), which obeys the scaling relation nu = 1/(2-zeta), and agrees with the finite-size-scaling exponent of fluctuations in the critical force. The velocity correlation function is non-universal at short distances.