  The mixed phase of layered superconductors with no magnetic screening is
studied through a partial duality analysis of the corresponding frustrated XY
model in the presence of weak random point pins. Isolated layers exhibit a
defective vortex lattice at low temperature that is phase coherent.
Sufficiently weak Josephson coupling between adjacent layers results in an
entangled vortex solid that exhibits weak superconductivity across layers. The
corresponding vortex liquid state shows an inverted specific heat anomaly that
we propose accounts for that seen in YBCO. A three-dimensional vortex lattice
with dislocations occurs at stronger coupling. This crossover sheds light on
the apparent discrepancy concerning the observation of a vortex-glass phase in
recent Monte Carlo simulations of the same XY model.
