Energy Landscapes in Random Systems, Driven Interfaces, and Wetting

We discuss the zero-temperature susceptibility of elastic manifolds with quenched randomness. It diverges with system size due to low-lying local minima. The distribution of energy gaps is deduced to be constant in the limit of vanishing gaps by comparing numerics with a probabilistic argument. The typical manifold response arises from a level-crossing phenomenon and implies that wetting in random systems begins with a discrete transition. The associated “jump field” scales as $〈h〉\sim L^{-5\mathrm{}/3}$ and $L^{-2.2\mathrm{}}$ for $(1+1)$ and $(2+1)$ dimensional manifolds with random bond disorder.