Parity breaking and phase transition induced by a magnetic field in high $T_c$ superconductors

We suggest that the 2+1 dimensional Gross-Neveu model can give an effective field theory description of low-energy quasiparticles in high temperature superconductors. The magnetic catalysis of dynamical symmetry breaking is examined. The model shows that a magnetic field can induce a phase transition associated with parity breaking. In particular, it is intended to give an explanation of a second phase transition observed in a recent experiment by Krishana et al.