Degradation of phase coherence by defects in a two-dimensional vortex lattice

The thermodynamic nature of two-dimensional vortex matter is studied 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 nonzero 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 autocorrelation 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.