content_image/357395.jpg content_image/357400.jpg content_image/357401.jpg content_image/357402.jpg
<img src='content_image/357395.jpg'>

The filling fractions are shown for several µ/T up to log z$_{c}$ . From these plots, it appears that f is diverging at k = 0 as z approaches z$_{c}$ , suggestive of condensation to a superfluid. Let us refer to the maximum density then as the critical density 

The scaling function c is shown in Figure 15. The limiting value is 

<img src='content_image/357400.jpg'>

<img src='content_image/357401.jpg'>

which is considerably less than for a free boson with c = 1. The function b decreases to zero at T/µ → 0, and the limiting value is 

<img src='content_image/357402.jpg'>

The energy per particle scaling functions ξ and ˜ ξ are shown in Figures 16, 17. 31 

