### 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 |
---|---|

Article number | 345002 |

Journal | Journal of Physics A: Mathematical and Theoretical |

Volume | 52 |

Issue number | 34 |

DOIs | |

Publication status | Published - Aug 1 2019 |

### Fingerprint

### 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)

### Cite this

*Journal of Physics A: Mathematical and Theoretical*,

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

**Berezinskii-Kosterlitz-Thouless transition and criticality of an elliptic deformation of the sine-Gordon model.** / Defenu, N.; Bacsó, V.; Márián, I. G.; Nándori, I.; Trombettoni, A.

Research output: Contribution to journal › Article

*Journal of Physics A: Mathematical and Theoretical*, vol. 52, no. 34, 345002. https://doi.org/10.1088/1751-8121/ab31c5

}

TY - JOUR

T1 - Berezinskii-Kosterlitz-Thouless transition and criticality of an elliptic deformation of the sine-Gordon model

AU - Defenu, N.

AU - Bacsó, V.

AU - Márián, I. G.

AU - Nándori, I.

AU - Trombettoni, A.

PY - 2019/8/1

Y1 - 2019/8/1

N2 - 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.

AB - 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.

KW - general studies of phase transitions

KW - phase transitions: general studies

KW - renormalization group evolution of parameters

KW - renormalization group methods

UR - http://www.scopus.com/inward/record.url?scp=85072347794&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85072347794&partnerID=8YFLogxK

U2 - 10.1088/1751-8121/ab31c5

DO - 10.1088/1751-8121/ab31c5

M3 - Article

AN - SCOPUS:85072347794

VL - 52

JO - Journal of Physics A: Mathematical and Theoretical

JF - Journal of Physics A: Mathematical and Theoretical

SN - 1751-8113

IS - 34

M1 - 345002

ER -