Approaching Pomeranchuk instabilities from ordered phase: A crossing-symmetric equation method

We explore features of a 3D Fermi liquid near generalized Pomeranchuk instabilities using a tractable crossing-symmetric equation method. We approach the instabilities from the ordered ferromagnetic phase. We find “quantum multi-criticality” as approach to the ferromagnetic instability drives instability in other channel(s). It is found that a charge nematic instability precedes and is driven by Pomeranchuk instabilities in both the ℓ=0ℓ=0 spin and density channels.