2 research outputs found
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(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.Comment: 4 pages, 3 figures. corrected references and typo
Depinning exponents of the driven long-range elastic string
We perform a high-precision calculation of the critical exponents for the
long-range elastic string driven through quenched disorder at the depinning
transition, at zero temperature. Large-scale simulations are used to avoid
finite-size effects and to enable high precision. The roughness, growth, and
velocity exponents are calculated independently, and the dynamic and
correlation length exponents are derived. The critical exponents satisfy known
scaling relations and agree well with analytical predictions.Comment: 6 pages, 5 figure