  Motivated by the recent experiments with Rydberg atoms in an optical tweezer
array, we accurately map out the ground-state phase diagram of the
antiferromagnetic Ising model on a square lattice with longitudinal and
transverse magnetic fields using the quantum Monte Carlo method. For a small
but nonzero transverse field, the transition longitudinal field is found to
stay nearly constant. By scrutinizing the phase diagram, we have uncovered a
narrow region where the system exhibits reentrant transitions between the
disordered and antiferromagnetic phases when the transverse field increases.
Our phase diagram provides a useful benchmark for quantum simulation with the
Rydberg-atom system.
