The exact solution of the boundary sine-Gordon model is studied in the region where the scaling dimension of the boundary field $1 < \Delta < 1$. It is shown that at $\Delta > 2/3$ the infrared fixed point belongs to the universality class of the underscreened anisotropic Kondo model. The boundary contribution to the specific heat scales as $C \sim T^{ 2\Delta^{ -1} - 2}$ at small temperatures.
Categories: cond-mat