  Motivated by 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
remain nearly constant. By scrutinizing the phase diagram, we uncover a narrow
region where the system exhibits reentrant transitions between the disordered
and antiferromagnetic phases with increasing transverse field. Our phase
diagram provides a useful benchmark for quantum simulation of a Rydberg atom
system.
