  The spin, charge and pairing correlation functions for the ground state of
two-dimensional $t-J$ model are calculated by using the power method which
projects out the ground state from a variational wave function. ``Exact''
results are obtained for $10\times10$ and $8\times8$ lattices with low particle
densities.
  The results are surprisingly similar to that of one-dimensional $t-J$ model.
The phenomenology is almost perfectly correlated with the concept of
Tomonaga-Luttinger liquid and it is incompatible with traditional Fermi liquid
theory.
