content_image/364009.jpg content_image/364015.jpg content_image/364016.jpg content_image/364017.jpg
<img src='content_image/364009.jpg'>

and 

In terms of the density: 

<img src='content_image/364015.jpg'>

<img src='content_image/364016.jpg'>

It is important to note that although the energy per particle scaling function ξ approaches the free field value at low temperatures, the above behavior is very different from the free field case. In the latter, the scaling function c = − 6Li$_{2}$( − z ) /π $^{2}$, which gives the diverging behavior at very low temperature: 

<img src='content_image/364017.jpg'>

Finally, as µ/T → −∞ , y ≈ 1 + z , and c ≈ 6 z/π 2 and n ≈ mT z/ 2 π . This leads 

