Abstract
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.
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