Vacuum structure of $(\overline \psi \psi )^2_3$-model with accounting for the magnetic field and chemical potential

The phase structure of $(2+1)$-dimensional field theory with a quartic fermion interaction is investigated with accounting for the background magnetic field $H$ and chemical potential $\mu$. It is shown that there is a critical curvature $\mu=\mu_c(H)$, which separates the multitude of the points $(\mu,H)$ into two regions. In one of them the vacuum is chiral-symmetric, and in the other the symmetry is spontaneously broken. The behavior of the critical curvature at large and small magnitudes of a background field is analyzed.