GLYPH<Minus> 4.0 GLYPH<Minus> 3.5 GLYPH<Minus> 3.0 GLYPH<Minus> 2.5 GLYPH<Minus> 2.0 GLYPH<Minus> 1.5 0.05 0.10 0.15 0.20 Density for attractive bosons PSfrag replacements n/mT µ/T FIG. 13: Density of the attractive bosons as a function of µ/T . The origin of the axes is at (log z$_{c}$, 0). 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 33