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    Is XY a phase transition?Work on the transition led to the 2016 Nobel Prize in Physics being awarded to Thouless and Kosterlitz; Berezinskii died in 1981. The XY model is a two-dimensional vector spin model that possesses U (1) or circular symmetry. This system is not expected to possess a normal second-order phase transition.
    Does XY model have a ferromagnet-paramagnet phase transition?In three and higher dimensions the XY model has a ferromagnet-paramagnet phase transition. At low temperatures the spontaneous magnetization is nonzero: this is the ferromagnetic phase. As the temperature is increased, spontaneous magnetization gradually decreases and vanishes at a critical temperature.
    Does XY model have phase transitions at finite temperature?Indeed, like the one-dimensional Ising model, the one-dimensional XY model has no phase transitions at finite temperature. The same computation for periodic boundary condition (and still h = 0) requires the transfer matrix formalism, though the result is the same. (Click "show" at right to see the details of the transfer matrix formalism.)
    Is there a phase transition in the 2D XY spin model?The two-dimensional (2D) XY spin model is one of the most intensively studied due to it’s a paradigmatic example of phase transitions mediated by topological defects [ 1 – 4 ]. It is well known that there is a Berezinskii-Kosterlitz-Thouless (BKT) phase transition in the XY spin model.
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