ANISOTROPIC SCALING IN THRESHOLD CRITICAL-DYNAMICS OF DRIVEN DIRECTEDLINES

The dynamical critical behavior of a single directed line driven in a random medium near the depinning threshold is studied both analyticall y (by renormalization group) and numerically, in the context of a flux line in a type-II superconductor with a bulk current (J) over right a rrow. In the absence of transverse fluctuations, the system reduces to recently studied models of interface depinning. In most cases, the pr esence of transverse fluctuations is found not to influence the critic al exponents that describe longitudinal correlations. For a manifold w ith d=4-epsilon internal dimensions, longitudinal fluctuations in on i sotropic medium are described by a roughness exponent zeta(parallel to )=epsilon/3 to all orders in epsilon, and a dynamical exponent z(paral lel to)=2-2 epsilon/9+O(epsilon(2)). Transverse fluctuations have a di stinct and smaller roughness exponent zeta(perpendicular to)=zeta(para llel 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 correla tion length exponent. The predicted exponents agree well with numerica l results for a flux line in three dimensions. As in the case of inter face depinning models, anisotropy leads to additional universality cla sses. A nonzero Hall angle, which has no analogue in the interface mod els, also affects the critical behavior.