Long-range correlations at depinning transitions

Abstract

Semi-infinite systems are considered with long-range surface fields ∝B _z ^−(1+r) for large distancesz from the surface. The influence of such fields on the global phase diagram and on the critical singularities of depinning transitions is studied within Landau theory. For |B|→0, the correlation length ξ_∥ diverges as ξ_∥∝b ^−1/2 withb=|B‖ln|B‖^−(1+r). For finiteB, ξ_∥∣t∣^v∣ withv _∣=(2+r)/(2+2r) wheret measures the distance from bulk coexistence. In the latter case, a Ginzburg criterion leads to the upper critical dimensiond ^*=(2+3r)/(2+r).