0 5 10 15 20 25 30 0.5 1.0 1.5 2.0 Attractive fermions PSfrag replacements η/s µ/T FIG. 9: The ratio η/s as a function of µ/T . The horizontal line is 1 / 4 π . to exponential growth: lim µ/T →−∞ η s = − πT $_{2}$√$_{2}$$_{µ}$ e − µ/T = − mT $_{4}$√$_{2}$ 1 n log(2 πn/mT ) (82) VII. ATTRACTIVE BOSONS IN 2 DIMENSIONS Using the same definitions as for fermions in eq. (51), the integral equation for bosons is where the + ( − ) sign refers to repulsive (attractive) interactions. The scaling function c is now y = 1 ± 2 y log(1 − zy ) (83) c = 6 π 2 ( Li$_{2}$( zy ) + 1 2 (1 − y − $^{1}$) log(1 − zy ) ) (84) 29