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Kosterlitz–Thouless transition : ウィキペディア英語版
Kosterlitz–Thouless transition
The Kosterlitz–Thouless transition (KT transition), or Berezinsky–Kosterlitz–Thouless transition (BKT transition), is a phase transition in the two-dimensional (2-D) XY model. It is a transition from bound vortex-antivortex pairs at low temperatures to unpaired vortices and anti-vortices at some critical temperature. The transition is named for condensed matter physicists Vadim L'vovich Berezinskiĭ (Вади́м Льво́вич Берези́нский), John M. Kosterlitz and David J. Thouless. BKT transitions can be found in several 2-D systems in condensed matter physics that are approximated by the XY model, including Josephson junction arrays and thin disordered superconducting granular films. More recently, the term has been applied by the 2-D superconductor insulator transition community to the pinning of Cooper pairs in the insulating regime, due to similarities with the original vortex BKT transition.
==XY model==
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. This is because the expected ordered phase of the system is destroyed by transverse fluctuations, i.e. the Goldstone modes (see Goldstone boson) associated with this broken continuous symmetry, which logarithmically diverge with system size.
This is a specific case of what is called the Mermin–Wagner theorem in spin systems.
Rigorously the transition is not completely understood, but the existence of two phases was proved by and .

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