  The two-dimensional $t$-$J$ model in the ground state is investigated by the
power Lanczos method. The pairing-pairing correlation function for
$d_{x^2-y^2}$-wave symmetry is enhanced in the realistic parameter regime for
high-$T_c$ superconductors. The charge susceptibility $\chi_c$ shows divergent
behavior as $\chi_c\propto\delta^{-1}$ near half-filling for the doping
concentration $\delta$, indicating that the value of the dynamical exponent $z$
is four under the assumption of hyperscaling. The peak height of the spin
structure factor $S_{max}(Q)$ also behaves as $S_{max}(Q) \propto\delta^{-1}$
near half-filling, which leads to the divergence of the antiferromagnetic
correlation length $\xi_m$ as $\xi_m \propto\delta^{-1/2}$. The boundary of
phase separation is estimated on the basis of the Maxwell construction.
Numerical results are compared with experimental features observed in
high-$T_c$ cuprates.
