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)similar to V(F,T)t at large times, where the velocity vanishes according to the creep formula as V(F,T)similar to 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)similar to 1/tau(1+alpha), where the exponent alpha(F,T) vanishes as alpha(F,T)proportional to F-mu as F -> 0. Our conclusion is that in the small force region alpha(F,T)< 1, the divergence of the averaged trapping time iota=+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)similar to 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)=2/3 up to some large scale, becomes equal to zeta=1 at the largest scales.