%0 Journal Article %T Existence of Low-Temperature Critical Regime in 1D Luttinger Liquid with a Weak Link %A A. M. Tsvelik %J Physics %D 1995 %I arXiv %R 10.1088/0305-4470/28/23/005 %X 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. %U http://arxiv.org/abs/cond-mat/9502022v1