We study the finite-temperature behavior of a dilute Bose gas using projected Gross-Pitaevskii equation by comparing to that of quantum Monte Carlo calculation in a two dimensional homogeneous system. By investigating the behavior of the correlation function, obtained results indicate that projected Gross-Pitaevskii equation is effective model of the Bose atoms with the long wavelength at low temperatures including the superfluid transition temperature. As the demonstration in a two dimensional homogeneous system, we find that this model describe the characteristic of vortex excitation indicated the superfluid transition.
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