Magnetic catalysis of $P$-parity breakdown in a massive Gross-Neveu model and high-$T_c$ superconductivity

It is shown within the framework of the $(2+1)$-dimensional $P$-invariant massive Gross–Neveu theory that an external magnetic field induces a first-order phase transition that breaks the $P$ parity. The use of the obtained results in the description of magnetic phase transitions in high-$T_c$ superconductors is discussed.