An infinite-range model, involving an elastic manifold which was pulled through a random potential by a force, F, was analyzed. Attention was focused on inertial effects. When the inertial parameter, M, was small there was a continuous de-pinning transition from a small-F static phase to a large-F moving phase. When M was increased to a certain value, Mc, a novel tricritical point occurred. When M was greater than Mc, the de-pinning transition became discontinuous, with hysteresis. The distribution of discrete so-called avalanche-like events which appeared as the force was increased in the static phase, for M > Mc, exhibited an unusual mixture of first-order like and critical features.

Depinning with Dynamic Stress Overshoots - Mean Field Theory. J.M.Schwarz, D.S.Fisher: Physical Review Letters, 2001, 87[9], 096107 (3pp)