  The electronic system of the 1D Hubbard model is not stable due to Peierls
instability; the correlations are strong even for the weak Coulomb interaction.
The resulting strongly correlated state without Landau quisi--particle
excitations is known as the Luttinger liquid. Critical exponents of a
power--law dependence of correlation functions at low energies differ
substantially for the Luttinger and Fermi liquids. In this paper we evaluate
two critical exponents that define non--trivial behavior of the density of
electronic states at low frequences and the momentum distribution of the
occupation number nearby $k_F$.
