Instabilities of Fermi liquid

I found some interesting informations related to instabilities of fermi liquid.
Generally, Fermi liquid theory is very successful for single particle excitation in solids, but also it can have some phase transition into another state with some degree of order. Susceptibility is responsible for the phase transition in Fermi liquid. Some perturbation h is present in Fermi liquid which give the variation in O (charge, spin, current etc.), then (q,E) = xi(q,E) h(q,E), q = charge, E = energy. For E = 0 we observe the static perturbation and static response, so if there is increase in susceptibility then the small amount perturbation h can also effect the process. At a critical temperature Tc = 0 the susceptibility diverges so in this case a small perturbation would induce a finite response in the system. Now if the calculation is made over the susceptibility, there is prediction over the Fermi liquid phase, with symmetry, where the system wants to go with the change is temperature. This means the various quantities can diverge with the lower temperature (Tc). Lower the critical temperature the ground state breaks the symmetry. Hence the calculation made over the susceptibility does not hold any accuracy.