Magnetic Instability in a Parity Invariant 2D Fermion System

We consider the parity invariant (2+1)-dimensional QED where the matter is represented as a mixture of fermions with opposite spins. It is argued that the perturbative ground state of the system is unstable with respect to the formation of magnetized ground state. Carrying out the finite temperature analysis we show that the magnetic instability disappears in the high temperature regime.