  The thermodynamic nature of two-dimensional vortex matter is studied
theoretically through a duality analysis of the XY model over the square
lattice with low uniform frustration. A phase-coherent vortex lattice state is
found at low temperature if rigid translations are prohibited. It shows a
non-zero phase rigidity that is degraded exclusively by the creation of
dislocation pairs. The unbinding of such pairs causes the vortex lattice to
simultaneously lose phase coherence and to melt at a continuous
(Kosterlitz-Thouless) phase transition. General phase auto-correlation
functions are also computed, and these results are used to argue for the
existence of a continuous melting transition of vortex matter in layered
superconductors.
