Critical temperature and thermodynamic properties of a homogeneous dilute weakly interacting Bose gas within the improved Hartree-Fock approximation at finite temperature

By means of Cornwall-Jackiw-Tomboulis effective action approach we investigate a homogeneous dilute weakly interacting Bose gas at finite temperature in vicinity of critical region. A longstanding debate, the shift of critical temperature, is considered and obtained in the universal form $\mathrm{\Delta }{T}_C\mathrm{/}{T}_C^{(0)}=c{n}_0^{1\mathrm{/}3}{a}_s$ with constants $c$ and $a$. The non-condensate fraction is contributed by quantum fluctuations as well as thermal exitations and can be expressed in sum of three terms. These terms correspond to the quantum fluctuations, thermal fluctuations and both. Indeed, the specific heat capacity and critical exponents are calculated and in excellent agreement with those in previous works and experimental data.