  We discuss the finite-temperature properties of Bose-Einstein condensates
loaded on a 2D optical lattice. In an experimentally attainable range of
parameters the system is described by the XY model, which undergoes a
Berezinskii-Kosterlitz-Thouless (BKT) transition driven by the vortex pair
unbinding. The interference pattern of the expanding condensates provides the
experimental signature of the BKT transition: near the critical temperature,
the k=0 component of the momentum distribution sharply decreases.
