  The mixed phase of layered superconductors with no magnetic screening is
studied through a partial duality analysis of the corresponding XY model in the
presence of random pinning centers. 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 is a precursor to the weak superconductor.
