Semi-vortices and cluster-vorticity: new concepts in the Berezinskii-Kosterlitz-Thouless phase transition


  • Brandon Gómez Bravo Insituto de Ciencias Nucleares, UNAM
  • Bryan David Juárez Hernández Insituto de Ciencias Nucleares, UNAM
  • Wolfgang Bietenholz Instituto de Ciencias Nucleares, UNAM



2d XY model, essential phase transition, vortices, cluster algorithm


The Berezinski˘ı-Kosterlitz-Thouless (BKT) essential phase transition in the 2d XY model is revisited. Its mechanism is usually described by the (un)binding of vortex–anti-vortex (V–AV) pairs, which does, however, not provide a clear-cut quantitative criterion for criticality. Known sharp criteria are the divergence of the correlation length and a discontinuity of the helicity modulus. Here we propose and probe a new criterion: it is based on the concepts of semi-vortices and cluster vorticity, which are formulated in the framework of the multi-cluster algorithm that we use to simulate the 2d XY model


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How to Cite

Gómez Bravo B, Juárez Hernández BD, Bietenholz W. Semi-vortices and cluster-vorticity: new concepts in the Berezinskii-Kosterlitz-Thouless phase transition. Supl. Rev. Mex. Fis. [Internet]. 2022 Jun. 25 [cited 2022 Oct. 4];3(2):020724 1-6. Available from: