  We use the determinant Quantum Monte Carlo method (DQMC) to study the
interaction-driven semimetal to antiferromagnetic insulator transition in a
$\pi$-flux Hamiltonian with modulated hoppings, a model which has two species
of Dirac fermions. It is found that the critical interaction strength $U_c$ is
decreased by reducing the velocity of the outer Dirac cone, while the inner
cone velocity fixes the band width. Although $U_c$ is monotonic, at fixed
inverse temperature $\beta$ the antiferromagnetic (AF) structure factor has a
maximum as a function of the hopping modulation. We also study the
corresponding strong coupling (Heisenberg model) limit, where the sublattice
magnetization is enhanced by the alternation of the exchange couplings. The AF
order is shown to be non-monotonic, and maximal at an intermediate degree of
anisotropy, in qualitative agreement with the Hubbard model. These results
quantify the effect of the velocities on the critical interaction strength in
Dirac fermion systems and enable an additional degree of control which will be
useful in studying strong correlation physics in ultracold atoms in optical
lattices.
