Random walk in a two-dimensional self-affine random potential: Properties of the anomalous diffusion phase at small external force.

We study the dynamical response to an external force F for a particle performing a random walk in a two-dimensional quenched random potential of Hurst exponent H=1/2 . We present numerical results on the statistics of first-passage times that satisfy closed backward master equations. We find that there exists a zero-velocity phase in a finite region of the external force 0 View Article and Find Full Text PDF

Random walk in two-dimensional self-affine random potentials: strong-disorder renormalization approach.

We consider the continuous-time random walk of a particle in a two-dimensional self-affine quenched random potential of Hurst exponent H>0 . The corresponding master equation is studied via the strong disorder renormalization procedure introduced in Monthus and Garel [J. Phys.

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.

Critical points of quadratic renormalizations of random variables and phase transitions of disordered polymer models on diamond lattices.

We study the wetting transition and the directed polymer delocalization transition on diamond hierarchical lattices. These two phase transitions with frozen disorder correspond to the critical points of quadratic renormalizations of the partition function. (These exact renormalizations on diamond lattices can also be considered as approximate Migdal-Kadanoff renormalizations for hypercubic lattices.

Multifractal statistics of the local order parameter at random critical points: application to wetting transitions with disorder.

Disordered systems present multifractal properties at criticality. In particular, as discovered by Ludwig [A.W.