**ABSTRACTÂ **

The constrained path Monte Carlo method was used to solve the Hubbard model for strongly correlated electrons systems analytically in arbitrary dimensions for one, two and three dimensional lattices. The energy variations with electron filling, electron-electron correlation strength and time as well as the kinetic and potential energies of these system were studied. A competition between potential and kinetic energies as well as a reduction of the rate of increase of the potential energy with increasing correlation were observed. The degenerate states of the lattice systems at zero correlation and the increase in the energy separation of the states at higher correlation strengths were evident. The variation of the energy per site with correlation strength of different lattice sizes and dimensions were obtained at half filling. From these it was apparent that the most stable lattices were the smallest for all the different dimensions. For one dimension, the convergence of the results of the constrained path method with the exact non-linear field theory results was observed.

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