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 at finite temperature, which undergoes a Berezinskii-K osterlitz-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.
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