  We discuss the onset of irreversibility and entanglement of vortex lines in
high Tc superconductors due to point disorder and thermal fluctuations using a
simplified cage model. A combination of Flory arguments, known results from
directed polymers in random media, and a Lindemann criterion are used to
estimate the field and temperature dependence of irreversibility, mechanical
entanglement and thermal melting. The qualitative features of this dependence,
including its nonmonotonicity when disorder is sufficiently strong, are in good
agreement with recent experiments.
