Pomeranchuk-Nematic instability in the presence of a weak magnetic field

We analyze a two-dimensional Pomeranchuk-Nematic instability, trigger by the Landau parameter $F_2<0$, in the presence of a small magnetic field. Using Landau Fermi liquid theory in the isotropic phase, we analyze the collective modes near the quantum critical point $F_2=-1,\omega_c=0$ (where $\omega_c$ is the cyclotron frequency). We focus on the effects of parity symmetry breaking on the Fermi surface deformation. We show that, for studying the critical regime, the linear response approximation of the Landau-Silin equation is not sufficient and it is necessary to compute corrections at least of order $\omega_c^2$. Identifying the slowest oscillation mode in the disordered phase, we compute the phase diagram for the isotropic/nematic phase transition in terms of $F_2$ and $\omega_c$.