Figure 3
From: Asymptotic Pomeranchuk instability of Fermi liquids in half-filled Landau levels
Dependence of the integral I(n, l) in Eq. (28), evaluated numerically, on n. The angular momenta of the instabilities are \(l=2,3,4 \text{ and } 5\) (solid, long-dashed, short-dashed and dotted lines, respectively). Circles represent values obtained using the effective potentials, \(v_n(\zeta )\) for \(n=1, 2\) and 3. Diamonds were obtained using the asymptotic formula in Eq. (26). The inset shows the behaviour at very large n for the \(l=2\) case. The straight line in the inset is a fit of the form \(I(n,l) = A_l/n^{B_l}\) to the numerical data for \(n \ge 800\). The fitting parameters are \(A_2 \approx 0.15\) and \(B_2 \approx 0.54\).
