### Abstract

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 language | English |
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Article number | 345002 |

Journal | Journal of Physics A: Mathematical and Theoretical |

Volume | 52 |

Issue number | 34 |

DOIs | |

Publication status | Published - Aug 1 2019 |

### Keywords

- 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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## Cite this

*Journal of Physics A: Mathematical and Theoretical*,

*52*(34), [345002]. https://doi.org/10.1088/1751-8121/ab31c5