Striped phases in two-dimensional dipole systems

Alessandro Giuliani, Joel L. Lebowitz, Elliott H. Lieb

Research output: Contribution to journalArticlepeer-review

32 Scopus citations


We prove that a system of discrete two-dimensional (2D) in-plane dipoles with four possible orientations, interacting via a three-dimensional (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 ferromagnetic ground state, when the ferromagnetic 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.

Original languageEnglish (US)
Article number184426
JournalPhysical Review B - Condensed Matter and Materials Physics
Issue number18
StatePublished - Nov 20 2007

All Science Journal Classification (ASJC) codes

  • Electronic, Optical and Magnetic Materials
  • Condensed Matter Physics


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