Effective Potential for Uniform Magnetic Fields through Pauli Interaction

We have calculated the explicit form of the real and imaginary parts of the effective potential for uniform magnetic fields which interact with spin-1/2 fermions through the Pauli interaction. It is found that the non-vanishing imaginary part develops for a magnetic field stronger than a critical field, whose strength is the ratio of the fermion mass to its magnetic moment. This implies the instability of the uniform magnetic field beyond the critical field strength to produce fermion pairs with the production rate density $w(x)=\frac{m^{4}}{24\pi}(\frac{|\mu B|}{m}-1)^{3}(\frac{|\mu B|}{m}+3)$ in the presence of Pauli interaction.