ABSTRACT
This chapter shows that the density and ferromagnetic instabilities were associated with the divergence of the respective response functions. It presents the proof of the second Pomeranchuk stability condition. These conditions were derived by Pomeranchuk in 1958, soon after L. Landau published his landmark Fermi liquid papers. When these conditions are not satisfied, the resulting instability is known as a Pomeranchuk instability. Exchange interaction of the electrons reduces the energy cost of the deformation of the Fermi surface associated with unequal populations of electrons with opposite spin polarizations. For a sufficiently large exchange interaction, the energy cost of this deformation turns negative, leading to appearance of a nonzero spin polarization. Equality is possible in certain pathological cases where charge and spin currents are both conserved.
