Self-organized interface growth with the negative nonlinearity in a random medium.

We introduce two self-organized growth models that describe the motion of the driven interfaces in random media including the Kardar-Parisi-Zhang (KPZ) nonlinearity. One model follows the quenched KPZ equation with a positive nonlinear term, while the other model follows the quenched KPZ equation with a negative nonlinear term. By obtaining the critical exponents for two models, we confirm that the sign of the KPZ nonlinear term does not affect the universality class.