Phase transitions in the $O(N)$ model with several coupling constants

Phase transformations of four-fermionic two-dimensional model (1) with several coupling constants are investigated in the leading order of $1/N$ expansion in the presence of non-zero temperature $T$ and chemical potential $\mu$. It is shown that at sufficiently large $T$ or $\mu$, the chiral invariance, spontaneously broken at $T$, $\mu=0$, is restored irrespective of values taken by the invariant constants. Critical values of the temperature and chemical potential are found.