Order in the ground state of a simple cubic dipole lattice in an external field

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 standard, linear dipole-field 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 a period of two lattice sites. Using a 1000-dipole lattice as a unit cell in numerical simulations of an infinite simple cubic lattice, we determine the ground state dipole configurations in the presence of an external field. We then analyze the polarization, dipole orientation statistics and correlations in these configurations. Our 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 under the influence of the external field. More specifically, for a general field direction, a sudden transition from two-site-periodic configurations to irregular configurations occurs at a finite value of the applied field strength.