Equation of state of an interacting Bose gas at finite temperature: a   Path Integral Monte Carlo study
  By using exact Path Integral Monte Carlo methods we calculate the equation of state of an interacting Bose gas as a function of temperature both below and above the superfluid transition. The universal character of the equation of state for dilute systems and low temperatures is investigated by modeling the interatomic interactions using different repulsive potentials corresponding to the same s-wave scattering length. The results obtained for the energy and the pressure are compared to the virial expansion for temperatures larger than the critical temperature. At very low temperatures we find agreement with the ground-state energy calculated using the diffusion Monte Carlo method. 
S. Pilati, K. Sakkos, J. Boronat, J. Casulleras and S. Giorgini