| We explore features of a Fermi liquid near generalized Pomeranchuk instabilities (PIs) starting from both ordered and disordered phases. These PIs can be viewed as quantum critical points in parameter space, and thus provide an alternate viewpoint on quantum criticality. We employ the tractable crossing symmetric equation method, which is a non-perturbative diagrammatic many-particle method used to calculate the Fermi liquid interaction functions and scattering amplitudes. We consider both repulsive and attractive underlying interactions of arbitrary strength. Starting from a ferromagnetically ordered ground state, we find that upon approach to an s-wave instability in one critical channel, the system simultaneously approaches instabilities in non-critical channels. We study origins and implications of this "quantum multicriticality". We also find that a nematic (non-s-wave) instability precedes and is driven by Pomeranchuk instabilities in both the s-wave spin and density channels. Finally, we discuss potential applications of our results to physical systems, such as ferromagnetic superconductors. |
