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Communications in Theoretical Physics

Renormalization Group Study of Ising Transition in Double-Frequency sine-Gordon Model

Ye Fei, Guo-Hui Ding, Xu Bo-wei

Published Aug 15, 2003• 2 citations
Publisher

Abstract

We utilize the renormalization group (RG) technique to analyze the Ising critical behavior in the double frequency sine-Gordon model. The one-loop RG equations obtained show unambiguously that there exist two Ising critical points besides the trivial Gaussian fixed point. The topology of the RG flows is obtained as well.
DOI
10.1088/0253-6102/40/2/169

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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.