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

TL;DR

This study explores the ground state configurations of a simple cubic lattice of dipoles under external fields, revealing degeneracy, periodicity, and complex arrangements influenced by field direction.

Contribution

It provides a numerical analysis of the ground state of dipole lattices under external fields, highlighting the effects on periodicity and configuration complexity.

Findings

Ground state is infinitely degenerate without external field.

External field direction affects dipole configuration periodicity.

Complex dipole arrangements form under general external field directions.

Abstract

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.