Driven interfaces in random media at finite temperature : is there an anomalous zero-velocity phase at small external force ?
| dc.creator | Monthus, Cecile | |
| dc.creator | Garel, Thomas | |
| dc.date | 2008-03-28 | |
| dc.date | 2008-10-08 | |
| dc.date.accessioned | 2026-07-07T10:15:06Z | |
| dc.date.available | 2026-07-07T10:15:06Z | |
| dc.description | The motion of driven interfaces in random media at finite temperature $T$ and small external force $F$ is usually described by a linear displacement $h_G(t) \sim V(F,T) t$ at large times, where the velocity vanishes according to the creep formula as $V(F,T) \sim e^{-K(T)/F^μ}$ for $F \to 0$. In this paper, we question this picture on the specific example of the directed polymer in a two dimensional random medium. We have recently shown (C. Monthus and T. Garel, arxiv:0802.2502) that its dynamics for F=0 can be analyzed in terms of a strong disorder renormalization procedure, where the distribution of renormalized barriers flows towards some "infinite disorder fixed point". In the present paper, we obtain that for small $F$, this "infinite disorder fixed point" becomes a "strong disorder fixed point" with an exponential distribution of renormalized barriers. The corresponding distribution of trapping times then only decays as a power-law $P(τ) \sim 1/τ^{1+α}$, where the exponent $α(F,T)$ vanishes as $α(F,T) \propto F^μ$ as $F \to 0$. Our conclusion is that in the small force region $α(F,T)<1$, the divergence of the averaged trapping time $\barτ=+\infty$ induces strong non-self-averaging effects that invalidate the usual creep formula obtained by replacing all trapping times by the typical value. We find instead that the motion is only sub-linearly in time $h_G(t) \sim t^{α(F,T)}$, i.e. the asymptotic velocity vanishes V=0. This analysis is confirmed by numerical simulations of a directed polymer with a metric constraint driven in a traps landscape. We moreover obtain that the roughness exponent, which is governed by the equilibrium value $ζ_{eq}=2/3$ up to some large scale, becomes equal to $ζ=1$ at the largest scales. | |
| dc.description | v3=final version | |
| dc.identifier | https://arxiv.org/abs/0803.4125 | |
| dc.identifier | http://arxiv.org/abs/0803.4125 | |
| dc.identifier | Phys. Rev. E 78, 041133 (2008) | |
| dc.identifier | doi:10.1103/PhysRevE.78.041133 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/173071 | |
| dc.subject | Disordered Systems and Neural Networks | |
| dc.title | Driven interfaces in random media at finite temperature : is there an anomalous zero-velocity phase at small external force ? | |
| dc.type | text |