Striped phases in two dimensional dipole systems

TL;DR

This paper rigorously proves the existence of striped ground states in 2D dipole systems with discrete orientations, analyzing how interactions influence ground state configurations and phase transitions.

Contribution

It provides the first rigorous proofs of striped ground states and reorientation transitions in 2D dipole systems with discrete orientations and specific interactions.

Findings

Striped ground states exist in 2D dipole systems with four orientations.

Increasing ferromagnetic strength enlarges stripe size, leading to ferromagnetism.

Antiferromagnetic interactions cause reorientation from in-plane to out-of-plane states.

Abstract

We prove that a system of discrete 2D in-plane dipoles with four possible orientations, interacting via a 3D dipole-dipole interaction plus a nearest neighbor ferromagnetic term, has periodic striped ground states. As the strength of the ferromagnetic term is increased, the size of the stripes in the ground state increases, becoming infinite, i.e., giving a ferromagentic ground state, when the ferromagentic interaction exceeds a certain critical value. We also give a rigorous proof of the reorientation transition in the ground state of a 2D system of discrete dipoles with six possible orientations, interacting via a 3D dipole-dipole interaction plus a nearest neighbor antiferromagnetic term. As the strength of the antiferromagnetic term is increased the ground state flips from being striped and in-plane to being staggered and out-of-plane. An example of a rotator model with a sinusoidal ground state is also discussed.