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We have studied needle shaped three-dimensional classical spin systems withpurely dipolar interactions in the microcanonical ensemble, using bothnumerical simulations and analytical approximations. We have observedspontaneous magnetization for different finite cubic lattices. The transitionfrom the paramagnetic to the ferromagnetic phase is shown to be first-order.For two lattice types we have observed magnetization flips in the phasetransition region. In some cases, gaps in the accessible values ofmagnetization appear, a signature of the ergodicity breaking found for systemswith long-range interactions. We analytically explain these effects byperforming a nontrivial mapping of the model Hamiltonian onto a one-dimensionalIsing model with competing antiferromagnetic nearest-neighbor and ferromagneticmean-field interactions. These results hint at performing experiments onisolated dipolar needles in order to verify some of the exotic properties ofsystems with long-range interactions in the microcanonical ensemble.

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