  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 +
random potential. We use the variational approximation to show that point and
columnar disorder have an 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.
