Dipolar needles in the microcanonical ensemble: Evidence of spontaneous magnetization and ergodicity breaking

¹ Department of Physics, Faculty of Exact and Natural Sciences, Tbilisi State University - 0128 Tbilisi, Georgia
² Department of Physics, The University of Texas at Austin - Austin TX 78712, USA
³ Laboratoire de Physique de l'ENS Lyon, Université de Lyon, CNRS - 46, allée d'Italie, 69007 Lyon, France
⁴ Max-Planck Institute for the Physics of Complex Systems-Nöthnitzer Str. 38, 01187 Dresden, Germany
⁵ Dipartimento di Fisica e Astronomia and CSDC, Università di Firenze, CNISM and INFN via G. Sansone, 1, Sesto Fiorentino, Italy

Received: 16 August 2013
Accepted: 10 October 2013

Abstract

We have studied needle-shaped three-dimensional classical spin systems with purely dipolar interactions in the microcanonical ensemble, using both numerical simulations and analytical approximations. We have observed spontaneous magnetization for different finite cubic lattices. The transition from the paramagnetic to the ferromagnetic phase is shown to be of first order. For two lattice types we have observed magnetization flips in the phase transition region. In some cases, gaps in the accessible values of magnetization appear, a signature of the ergodicity breaking found for systems with long-range interactions. We analytically explain these effects by performing a nontrivial mapping of the model Hamiltonian onto a one-dimensional Ising model with competing antiferromagnetic nearest-neighbor and ferromagnetic mean-field interactions. These results hint at performing experiments on isolated dipolar needles in order to verify some of the exotic properties of systems with long-range interactions in the microcanonical ensemble.