The equal-time pairing correlation function of the two-dimensional t-J model on a square lattice is studied using a high-temperature expansion method. The sum of the pairing correlation, its spatial dependence, and the correlation length are obtained as functions of temperature down to
T≃0.2t. By comparison of single-particle contributions in the correlation functions, we find an effective attractive interaction between quasi-particles in
dx2−y2-wave pairings. It is shown that d-wave correlation grows rapidly at low temperatures for 0.5 < n < 0.9, with n being the electron density. The temperature for this growth is roughly scaled by J/2. This is in sharp contrast to the Hubbard model in a weak or intermediate coupling region, where there is no numerical evidence of superconductivity.
Two-dimensional t-J model is studied by a variational Monte Carlo method, using Gutzwiller-Jastrow-type wave functions. Various kinds of superconducting pairing symmetries are compared in order to determine the phase diagram of the ground state in the full J/t-n plane. Near the half filling where the high temperature superconductivity is expected, the d_{x^2-y^2} wave pairing state is always the most stable among various symmetries. The three-site term hardly changes the phase diagram in this regime. In the low electron density, the extended s-type wave becomes a quantitatively good state for large J/t, although the energy gain is small. The Gutzwiller wave function is shown to be the exact ground state in the low-electron-density limit for the supersymmetric case (J/t=2).