Excitonic pairing between nodal fermions

We discuss excitonic pairing in nodal fermion systems, characterized by a vanishing quasiparticle density of states at the point-like Fermi surface and a concomitant lack of screening for long-range interactions. We solve the gap equation and obtain the free energy and critical values of the interaction strength for a variety of algebraically interactions and power-law densities of states. On the basis of this insight, we analyze possible phase transitions in this interesting class of non-fermi-liquid systems.