Phase transitions of the flux-line lattice in high-temperature superconductors with weak columnar and point disorder

We study the effects of weak point and columnar disorder on the vortex-lattice phase transitions in high-temperature superconductors. The combined effect of thermal fluctuations and of quenched disorder is investigated using a simplified cage model. For point disorder we use the mapping to a directed polymer in a disordered medium in 2 + 1 dimensions. For columnar disorder the problem is mapped into a quantum particle in a harmonic and a random potential. We use the variational approximation to show that point and columnar disorder have opposite effect on the position of the melting line as is observed experimentally. For point disorder, replica symmetry breaking plays a role at the transition into a vortex glass at low temperatures.