Long-range correlations at depinning transitions

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 diverges as b^–1/2 withb=|Bln|B^–(1+r). For finiteB, 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).