Scaling theory of depinning in the Sneppen model

Abstract

We develop a scaling theory for the critical depinning behavior of the Sneppen interface model [Phys. Rev. Lett. 69, 3539 (1992)]. This theory is based on a ‘‘gap’’ equation that describes the self-organization process to a critical state of the depinning transition. All of the critical exponents can be expressed in terms of two independent exponents, ${\nu }_{\mathrm{\parallel }}$(d) and ${\nu }_{\mathrm{\perp }}$(d), characterizing the divergence of the parallel and perpendicular correlation lengths as the interface approaches its dynamical attractor.