Berezinskii-Kosterlitz-Thouless transition and criticality of an elliptic deformation of the sine-Gordon model
Year: 2019
Authors: Defenu N., Bacso V., Màriàn IG., Nàndori I., Trombettoni A.
Autors Affiliation: Heidelberg Univ, Inst Theoret Phys, D-69120 Heidelberg, Germany; Univ Debrecen, POB 105, H-4010 Debrecen, Hungary; MTA DE Particle Phys Res Grp, POB 51, H-4001 Debrecen, Hungary; MTA Atomki, POB 51, H-4001 Debrecen, Hungary; CNR IOM DEMOCRITOS Simulat Ctr, Via Bonomea 265, I-34136 Trieste, Italy; SISSA, Via Bonomea 265, I-34136 Trieste, Italy; Ist Nazl Fis Nucl, Sez Trieste, Via Bonomea 265, I-34136 Trieste, Italy.
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 sit one, are found to be of BKT type. Explicit expressions for the critical coupling as a function of the elliptic modulus are given.
Journal/Review: JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL
Volume: 52 (34) Pages from: 345002-1 to: 345002-17
More Information: The authors gratefully thank E Langmann, G Gori, G Mussardo, P Sodano, G Somogyi, G Takacs and T G Kovacs for useful discussions. AT is grateful for kind hospitality to the Galileo Galilei Institute (Florence) where part of this work has been performed during the Workshop ’From Static to Dynamical Gauge Fields with Ultracold Atoms’. Financial support by the Janos Bolyai Research Scholarship of the Hungarian Academy of Sciences and by the CNR/MTA Italy-Hungary 2019-2021 Joint Project ’Strongly interacting systems in confined geometries’ is gratefully acknowledged. ND acknowledges financial support by the Deutsche Forschungsgemeinschaft (DFG) under the Collaborative Research Centre ’SFB 1225 ISOQUANT’ and Germany’s Excellence Strategy EXC-2181/1-390900948 (the Heidelberg STRUCTURES Excellence Cluster)’.KeyWords: renormalization group evolution of parameters; phase transitions: general studies; general studies of phase transitions; renormalization group methodsDOI: 10.1088/1751-8121/ab31c5Citations: 2data from “WEB OF SCIENCE” (of Thomson Reuters) are update at: 2024-10-20References taken from IsiWeb of Knowledge: (subscribers only)