Creep dynamics of elastic manifolds via exact transition pathways

Abstract

We study the steady state of driven elastic strings in disordered media below the depinning threshold. In the low-temperature limit, for a fixed sample, the steady state is dominated by a single configuration, which we determine exactly from the transition pathways between metastable states. We obtain the dynamical phase diagram in this limit. At variance with a thermodynamic phase transition, the depinning transition is not associated with a divergent length scale of the steady state below threshold, but only of the transient dynamics. We discuss the distribution of barrier heights, and check the validity of the dynamic phase diagram at small but finite temperatures using Langevin simulations. The phase diagram continues to hold for broken statistical tilt symmetry. We point out the relevance of our results for experiments of creep motion in elastic interfaces.

Nonsteady relaxation and critical exponents at the depinning transition

“…It is worth noting here that while h −ν can be associated with the geometrical correlation length ξ diverging in lim f → f + c in the steady state, this is not true in lim f → f − c . We can, however, find a divergent correlation length relax ∼ (f c − f ) −ν , not observed in the steady-state geometry, but associated with the deterministic part of the avalanches that are produced in the steady-state dynamics of the f < f c low-temperature creep regime [13,14]. Hence, the interpretation of Eq.…”

“…At finite temperature and for f f c , the system presents an ultraslow steady-state creep motion with universal features [4,33,34] directly correlated with geometrical crossovers [13,35]. At very small temperatures the monotonic increase of the correlation length with decreasing f below f c shows that the naive analogy breaks, and that depinning must be regarded as a nonstandard phase transition [13,14]. The transition is then smeared out, with the velocity vanishing as v ∼ T ψ exactly at f = f c , with ψ the so-called thermal rounding exponent [36][37][38][39][40].…”

“…(1) nor directly invert the nonlinear system of Eq. (14). In the following section we use such an algorithm [10,11] to study the finite-size effects on f s c and in particular to obtain the appropriate thermodynamic limit f c = lim (L,M)→∞ f s c controlling the universal nonsteady relaxation.…”

“…From a purely theoretically point of view, considerable progress has been made in recent years thanks to a fruitful interplay between the very powerful analytical [3][4][5] and numerical techniques specially developed for studying equilibrium [6,7], depinning [8][9][10][11][12], and creep [13,14] of strictly elastic manifolds. From the experimental viewpoint, on the other hand, the understanding of this particular problem is directly relevant for various experimental situations where the elastic approximation is well met, such as magnetic [15][16][17][18] or ferroelectric domain walls [19][20][21][22], contact lines in wetting [23,24], and fractures [25,26].…”

Domain Wall Roughness in Stripe PhaseBiFeO3Thin Films

“…This value can be strongly under-or overestimated by different analysis methods [31], and is especially prob- lematic for values close to ζ ∈ N. To verify the high ζ value we obtained from the roughness function B(r), we therefore used the Fourier transformû(q) of the displacement u(r) −ū from its mean valueū to compute the monoaffine structure factor [35][36][37]:…”