Line-delocalization transitions in the presence of quenched disorder

We classify universality classes and all possible critical singularities for line-delocalization transitions in a space of arbitrary dimensionality in the presence of quenched disorder uncorrelated along the line direction but otherwise general. The situation under consideration involves both one-line unbinding (e.g., the wetting transition in two dimensions) and many-line delocalization (e.g., the appearance of Abrikosov flux lines near the lower critical field in disordered type-II superconductors). In particular, we find that any unbinding transition from a short-ranged pinning potential in two dimensions is characterized by a ''classical'' jump in the specific heat. We also reproduce many of the results of R. Lipowsky and M. E. Fisher [Phys. Rev. Lett. 56, 472 (1986)] and characterize their ranges of validity. We find, however, that the crossover exponent for the two-dimensional critical wetting transition in the presence of random bond disorder is 5, rather than 4. For the cases in which comparison is possible our results are in agreement with exact replica calculations.