content_image/360745.jpg
<img src='content_image/360745.jpg'>

## VIII. REPULSIVE FERMIONS AND BOSONS IN 2 DIMENSIONS 

## A. Fermions 

There are solutions to the eq. (53) for all µ/T < 0, and the density is positive in this range. A plot of the density is shown in Figure 18. The density maximizes at µ/T ≈ − 0 . 56, where n/mT ≈ 0 . 04. This seems physically reasonable given the strong repulsion in the unitary limit. In contrast, for small coupling g , the kernel G ≈ − g , and there are solutions for positive chemical potential. In the bosonic case, our formalism leads to a critical density of n$_{c}$ = mT 2 π log(2 π/mg ) for the Kosterlitz- Thouless transition[20]. The filling fractions are shown in Figure 19. Note that they are considerably smaller than in the attractive case, as expected. The scaling 

