  The nature of decoupling in the mixed phase of extremely type-II layered
superconductors is studied theoretically through a duality transformation of
the layered XY model with frustration. In the limit of weak coupling, we
generally find that the Josephson effect is absent if and only if the phase
correlations within isolated layers are short range. In the case specific to
uniform frustration, we notably identify a decoupled pancake vortex liquid
phase that is bounded by first-order and second-order decoupling lines in the
magnetic field vs. temperature plane. These transitions potentially account for
the flux-lattice melting and for the flux-lattice depinning that is observed in
clean high-temperature superconductors.
