16 research outputs found
Berezinskii-Kosterlitz-Thouless transition and criticality of an elliptic deformation of the sine-Gordon model
We introduce and study the properties of a periodic model interpolating
between the sine-- and the sinh--Gordon theories in 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.Comment: v2, 10 pages, 8 figures, accepted in J. Phys.
c-function and central charge of the sine-Gordon model from the non-perturbative renormalization group flow
In this paper we study the c-function of the sine-Gordon model taking explicitly into account the periodicity of the interaction potential. The integration of the c-function along trajectories of the non-perturbative renormalization group flow gives access to the central charges of the model in the fixed points. The results at vanishing frequency \u3b22, where the periodicity does not play a role, are retrieved and the independence on the cutoff regulator for small frequencies is discussed. Our findings show that the central charge obtained integrating the trajectories starting from the repulsive low-frequencies fixed points (\u3b22<8\u3c0) to the infra-red limit is in good quantitative agreement with the expected \u3b4c=1 result. The behavior of the c-function in the other parts of the flow diagram is also discussed. Finally, we point out that including also higher harmonics in the renormalization group treatment at the level of local potential approximation is not sufficient to give reasonable results, even if the periodicity is taken into account. Rather, incorporating the wave-function renormalization (i.e. going beyond local potential approximation) is crucial to get sensible results even when a single frequency is used