Berezinskii-Kosterlitz-Thouless transition and criticality of an elliptic deformation of the sine-Gordon model

N. Defenu, V. Bacsó, I. G. Márián, I. Nándori, A. Trombettoni

Research output: Contribution to journalArticle


We introduce and study the properties of a periodic model interpolating between the sine-And the sinh-Gordon theories in 1 + 1 dimensions. This model shows the peculiarities, due to the preservation of the functional form of their potential across RG flows, of the two limiting cases: The sine-Gordon, not having conventional order/magnetization at finite temperature, but exhibiting Berezinskii-Kosterlitz-Thouless (BKT) transition; and the sinh-Gordon, not having a phase transition, but being integrable. The considered interpolation, which we term as sn-Gordon model, is performed with potentials written in terms of Jacobi functions. The critical properties of the sn-Gordon theory are discussed by a renormalization-group approach. The critical points, except the sinh-Gordon one, are found to be of BKT type. Explicit expressions for the critical coupling as a function of the elliptic modulus are given.

Original languageEnglish
Article number345002
JournalJournal of Physics A: Mathematical and Theoretical
Issue number34
Publication statusPublished - Aug 1 2019


  • general studies of phase transitions
  • phase transitions: general studies
  • renormalization group evolution of parameters
  • renormalization group methods

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Statistics and Probability
  • Modelling and Simulation
  • Mathematical Physics
  • Physics and Astronomy(all)

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