2-D Bose-Einstein condensates BKT transition. A gas of atoms arranged in a single, flat layer ordinarily has 'thermal' behavior (left) in which the atoms act as individual entities. At lowered temperatures, the gas transforms into a quasi-condensate (middle) consisting of little islands (schematically represented as colored blobs) that fluctuate in time; within each island atoms act as a single coordinated entity. At lower temperatures still, the gas enters the superfluid BKT phase (right): the islands start to coalesce and atoms can flow frictionlessly within the merged area. The Kosterlitz-Thouless transition, or Berezinsky-Kosterlitz-Thouless transition, is a phase transition in the 2D XY model. It is a transition from bound vortex-antivortex pairs at low temperatures to unpaired vortices and anti-vortices at some critical temperature.