Anisotropic scaling in threshold critical dynamics of driven directed lines

The dynamical critical behavior of a single directed line driven in a random medium near the depinning threshold is studied both analytically (by renormalization group) and numerically, in the context of a flux line in a type-II superconductor with a bulk current (J) over right arrow. In the absence of transverse fluctuations, the system reduces to recently studied models of interface depinning. In most cases, the presence of transverse fluctuations is found not to influence the critical exponents that describe longitudinal correlations. For a manifold with d=4-epsilon internal dimensions, longitudinal fluctuations in on isotropic medium are described by a roughness exponent zeta(parallel to)=epsilon/3 to all orders in epsilon, and a dynamical exponent z(parallel to)=2-2 epsilon/9+O(epsilon(2)). Transverse fluctuations have a distinct and smaller roughness exponent zeta(perpendicular to)=zeta(parallel to)-d/2 for an isotropic medium. Furthermore, their relaxation is much slower, characterized by a dynamical exponent z(perpendicular to)=z(parallel to)+1/nu, where nu=1/(2-zeta(parallel to)) is the correlation length exponent. The predicted exponents agree well with numerical results for a flux line in three dimensions. As in the case of interface depinning models, anisotropy leads to additional universality classes. A nonzero Hall angle, which has no analogue in the interface models, also affects the critical behavior.