  Motivated by the presence of a lattice of rotating molecular dipoles in the
high temperature phase of methylammonium lead iodide, we investigate the ground
state of a simple cubic lattice of dipoles interacting with each other via the
dipole-dipole interaction and with an external field via the Zeeman
interaction. In the absence of an external field, the ground state is
infinitely degenerate, and all the configurations in the ground state manifold
are periodic along the three lattice axes with period 2. We numerically
determine the ground state of a 1000-dipole lattice interacting with an
external field, and we analyze the polarization, dipole orientation statistics
and correlations in this state. These calculations show that for some special
directions of the external field the two-site periodicity in the dipole
configurations is preserved, while in the general case this periodicity is lost
and complex dipole configurations form in the presence of the external field.
