Effects due to finite values of the temperature and the chemical potential in some two-dimensional field models

In the mean field approximation the structure of ground state is investigated in the $N\to\infty$ Gross–Neveu model and two-dimensional $\varphi^4$ model with fermions finite temperature $T$ and chemical potential of fermions $\alpha$. Critical values $T_c$ and $\alpha_c$ are obtained. It is found that the symmetry which is broken at $T=\alpha 0$ can be restored by means of raising $T$ or $\alpha$ above critical values. The possibility of using the results in the description of physical properties of quasi-one-dimensional systems in the theory of condensed matter is discussed.