Competing effects of point versus columnar defects on the roughening of directed polymers in random media

Inspired by recent experiments on cuprate superconductors investigating the enhanced pinning of vortex lines, we have performed transfer matrix studies of directed polymers in random media subject to both point and columnar defects, focusing our attention on the competition between these two different types of disorder. We find that the positional fluctuations in a mixed random medium are larger than in the case of purely columnar or point defects, and show via Flory arguments that the asymptotic behavior is sub-ballistic, x∼t/(lnt${)}^{\mathrm{\psi }}$, with ψ=2 (ψ≊1.60) in 1+1 (2+1) dimensions.