QED vacuum fluctuations as a function of magnetic moment

Precision QED experiments (muon $g-2$ and muonic protium Lamb shift) suggest closer examination of QED in the case $g>2$. We evaluate the non-perturbative one-loop effective potential in a quasi-constant external electromagnetic field as a function of the magnetic moment. For $|g|>2$, the lowest magnetic Landau levels become unstable, which is treated by recognizing periodicity of the Landau spectrum as a function of $g$. This instability leads to a cusp in the effective potential at the periodic points $g=2,-2,6,-6...$ Where the cusp is present, the beta function and light-light scattering coefficients differ from their perturbative values. We extract the nonperturbative form of the beta function as a function of $g$ and show that QED displays asymptotic freedom for a specific range of $g$.