In the framework of the functional renormalization group method it is shown
that the phase structure of the 2-dimensional sine-Gordon model possesses a
nontrivial UV fixed point which makes the model asymptotically safe. The fixed
point exhibits strong singularity similarly to the scaling found in the
vicinity of the infrared fixed point. The singularity signals the upper
energy-scale limit to the validity of the model. We argue that the sine-Gordon
model with a momentum-dependent wavefunction renormalization is in a dual
connection with the massive sine-Gordon model.Comment: 8 pages, 3 figure
