Magnetic Catalysis of the $\operatorname{P}$-Parity-Breaking Phase Transition of the First Order and High-Temperature Superconductivity

In the framework of a $(2+1)$-dimensional $\operatorname{P}$-even gauge theory based on the massive Gross–Neveu model, we show that an external magnetic field induces the P-parity-breaking phase transition of the first order. A dynamical generation of the Chern–Simons term and fractional particle spin and statistics occurs at the critical point. The results in the paper can be interesting in connection with recently discovered phase transitions in high-temperature superconductors.