Transition temperature of the homogeneous and dilute Bose gas in D-dimensions
arXiv:0707.1538
Abstract
The phase transition temperature of the homogeneous and dilute Bose gas in D-dimensions () is calculated by a mean field-based statistical method. The shift of the phase transition temperature is written up to the leading order as $ΔT_c/T_c^0 = c \gam^{\al}$, where $\gam=n^{1/3}a$. We derived Huang's result of the phase transition temperature in the generalized dimensions. We show that is positive and $\al(D)=2(D/2-1)^2$ in the short-wavelength range. The origin of the difference between $\al=1/2$ and $\al=1$ at D=3 is discussed. The at D=2 is calculated in the same scheme. The result is compared with Fisher and Hohenberg's KT temperature.
4 pages, 2 figure