Depinning in the quenched Kardar-Parisi-Zhang class. II. Field theory.

There are two main universality classes for depinning of elastic interfaces in disordered media: quenched Edwards-Wilkinson (qEW) and quenched Kardar-Parisi-Zhang (qKPZ). The first class is relevant as long as the elastic force between two neighboring sites on the interface is purely harmonic and invariant under tilting. The second class applies when the elasticity is nonlinear or the surface grows preferentially in its normal direction.

Depinning in the quenched Kardar-Parisi-Zhang class. I. Mappings, simulations, and algorithm.

Depinning of elastic systems advancing on disordered media can usually be described by the quenched Edwards-Wilkinson equation (qEW). However, additional ingredients such as anharmonicity and forces that cannot be derived from a potential energy may generate a different scaling behavior at depinning. The most experimentally relevant is the Kardar-Parisi-Zhang (KPZ) term, proportional to the square of the slope at each site, which drives the critical behavior into the so-called quenched KPZ (qKPZ) universality class.