Berezinskii-Kosterlitz-Thouless transition and criticality of an elliptic deformation of the sine-Gordon model - Defenu, Nicolò; Bacso, V.; Márián, István Gábor; Nándori, István; Trombettoni, Andrea (Journal of physics. A, Mathematical and theoretical, 2019)
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.
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