  We study the phase diagram of the two-dimensional repulsive Hubbard model
with spin-dependent anisotropic hopping at half-filling. The system develops
Ising antiferromagnetic long-range order already at infinitesimal repulsive
interaction strength in the ground state. Outside the perturbative regime,
unbiased predictions for the critical temperatures of the Ising antiferromagnet
are made for representative interaction values by a variety of state-of-the-art
quantum Monte Carlo methods, including the diagrammatic Monte Carlo,
continuous-time determinantal Monte Carlo and path-integral Monte Carlo
methods. Our findings are relevant to ultracold atom experiments in the
p-orbital or with spin-dependent optical lattices.
