  A quantum Monte Carlo simulation method has been developed and applied to
study the critical behavior of a single Kondo impurity in a Luttinger liquid.
This numerically exact method has no finite-size limitations and allows to
simulate the whole temperature range. Focusing on the impurity magnetic
susceptibility, we determine the scaling functions, in particular for
temperatures well below the Kondo temperature. In the absence of elastic
potential scattering, we find Fermi-liquid behavior for strong
electron-electron interactions, g_c < 1/2, and anomalous power laws for 1/2<g_c
< 1, where g_c is the correlation parameter of the Luttinger liquid. These
findings resolve a recent controversy. If elastic potential scattering is
present, we find a logarithmically divergent impurity susceptibility at g_c<1/2
which can be rationalized in terms of the two-channel Kondo model.
