Berezinskii–Kosterlitz–Thouless transition

In a two-dimensional XY model, each lattice site carries a planar spin whose direction can rotate continuously. At low temperatures, spin orientations are correlated over long distances, although the model does not have ordinary long-range magnetic order. The system can also contain vortices: around such a point defect, the spin direction winds around the circle. A vortex and an antivortex have opposite winding and, at low temperature, tend to occur as bound pairs.

As temperature increases, thermal fluctuations make it energetically possible for bound vortex–antivortex pairs to unbind. Above the transition, free vortices disrupt correlations across the system, producing a disordered phase. The change is driven by the creation and separation of topological defects, rather than by the usual onset or loss of a conventional local order parameter. In the ideal two-dimensional XY model, correlations in the low-temperature phase decay algebraically; the transition has characteristic essential, rather than ordinary power-law, singular behavior.

Vadim Berezinskii developed related ideas in the early 1970s. John Michael Kosterlitz and David Thouless independently developed the theory of topological ordering and transitions in two-dimensional systems. Their work showed how phase transitions could occur in systems where conventional long-range order is absent, and established the role of topological defects. Kosterlitz and Thouless shared half of the 2016 Nobel Prize in Physics with David J. Thouless, awarded for theoretical discoveries of topological phase transitions and topological phases of matter.

The transition is relevant to the two-dimensional XY model and provides a framework for understanding phenomena in thin superfluid films, superconducting films, and other two-dimensional systems. Real materials can include additional interactions, finite-size effects, disorder, or coupling to their surroundings, so their behavior need not match the ideal model in every detail. The BKT mechanism is therefore a specific class of transition, not a universal description of every phase change in two dimensions.