  We study quantum criticality of the magnetic field induced charge density
wave (CDW) order in correlated spinless Dirac fermions on the $\pi$-flux square
lattice at zero temperature as a prototypical example of the magnetic
catalysis, by using the infinite density matrix renormalization group. It is
found that the CDW order parameter $M(B)$ exhibits an anomalous magnetic field
$(B)$ scaling behavior characteristic of the $(2+1)$-dimensional chiral Ising
universality class near the quantum critical point, which leads to a strong
enhancement of $M(B)$ compared with a mean field result. We also establish a
global phase diagram in the interaction-magnetic field plane for the fermionic
quantum criticality.
