On a nonideal Bose gas model

We consider a polynomial generalization of the Huang-Davies model in the nonideal Bose gas theory. We prove that the Gaussian dominance condition is fulfilled for all values of the chemical potential. We show that the lower bound for the critical temperature in the Huang-Davies model obtained by the infrared bound method coincides with the exact value of this quantity in the Davies theory. Using the large deviation principle, we prove a possibility of a generalized Bose condensation in the polynomial model.