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

TL;DR

This paper introduces the sn-Gordon model, an elliptic deformation interpolating between sine- and sinh-Gordon theories, revealing BKT criticality and integrability properties through RG analysis.

Contribution

The paper presents a novel elliptic deformation of the sine-Gordon model, analyzing its critical behavior and RG flow, highlighting BKT transitions in a new interpolating framework.

Findings

Critical points are of BKT type, except the sinh-Gordon limit.

Explicit critical coupling expressions as a function of elliptic modulus.

The model preserves potential form across RG flows, linking two known theories.

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 {\em 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.