Critical exponents of the driven elastic string in a disordered medium

We analyze the harmonic elastic string driven through a continuous random potential above the depinning threshold. The velocity exponent $\beta =0.33\left(2\right)$ 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 $\nu =1.29\left(5\right)$, which obeys the scaling relation $\nu =1∕(2-\zeta )$, and agrees with ${\nu }_{\mathrm{FS}}$, the finite-size-scaling exponent of fluctuations in the critical force. Surprisingly, the velocity correlation function is nonuniversal at short distances.