Renormalization group analysis of weak collective pinning

The effect of impurity disorder on vortex lattices in type-II superconductors is studied within the framework of the weak collective pinning theory. Using a renormalization group approach, we calculate the size R(c) of collectively pinned vortex bundles in the regime a(o) < R(c) < lambda (small bundles) for isotropic superconductors. We assume weak disorder and neglect thermal effects. Our findings quantitatively refine the lowest-order perturbation result, R(c) proportional to exp(const.B-3/2)/root B, obtained by Larkin and Ovchinnikov in 1979 (B is the magnetic induction). In particular, we find a different numerical constant in the exponential as well as a new algebraic prefactor. These improvements provide us with a more accurate functional dependence of the critical current on the magnetic field.