A body-centered-cubic (BCC) lattice model with realistic many-body interactions is introduced and investigated by means of the Metropolis' Monte Carlo method to describe both crystalline and molten states of Si. Under the simplest assumption that atoms surrounded by tetrahedral first-neighbors only have an energy lower than the other atoms, a clear first-order phase transition including hysteresis is observed between a solid with diamond structure and a melt. Nucleation and domain growth are dynamically observed in certain range of the supercooling. In order to introduce more realistic and accurate lattice-gas models, the Tersoff potential is renormalized and the interactions are mapped onto a BCC lattice. Then, it is found that the phase transition temperature and other thermodynamic properties are dramatically improved compared with the case using the Tersoff potential directly in the lattice model without renormalization.