where A is the area of the flat region, L is the length of the cylinder and I is the average value of the auxiliary quantity I over the considered regions. The z-axis is defined as being along the ⃗ r direction, and points ⃗ k1, ⃗ k2 are respectively the lowest and highest points of the considered Fermi surface. Vectors ⃗ v1, ⃗ v2 are their respective z-axis-projected normal vectors (see Fig. ). Roth's et al. work proves that even though the quantum system is three-dimensional, if it does possess any lower-dimensional part of the Fermi surface (i.e. either a flat part or a cylindrical one), then the decay asymptotics of the RKKY interaction (and analogously of the Friedel oscillations) is dampened, meaning that they persevere for longer distances.