Glassy motion of an elastic string

Driven interfaces in random media at finite temperature: existence of an anomalous zero-velocity phase at small external force

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) approximately V(F,T)t at large times, where the velocity vanishes according to the creep formula as V(F,T) approximately e;{-K(T)F;{mu}} for F-->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, J. Phys. A 41, 255002 (2008)] 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(tau) approximately 1tau;{1+alpha} , where the exponent alpha(F,T) vanishes as alpha(F,T) proportional, variant F micro as F-->0 . Our conclusion is that in the small force region alpha(F,T)<1 , the divergence of the averaged trapping time tau[over ]=+infinity 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 sublinearly in time h{G}(t) approximately t;{alpha(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 zeta{eq}=23 up to some large scale, becomes equal to zeta=1 at the largest scales.

Creep motion of an elastic string in a random potential

We study the creep motion of an elastic string in a two-dimensional pinning landscape by means of Langevin dynamics simulations. We find that the velocity-force characteristics are well described by the creep formula predicted from phenomenological scaling arguments. We analyze the creep exponent mu and the roughness exponent zeta. Two regimes are identified: when the temperature is larger than the strength of the disorder, we find mu approximately 1/4 and zeta approximately 2/3, in agreement with the quasi-equilibrium-nucleation picture of creep motion; on the contrary, when lowering the temperature enough, the values of mu and zeta increase, showing a strong violation of the latter picture.