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

TL;DR

This study investigates dipolar needle-shaped spin systems in the microcanonical ensemble, revealing spontaneous magnetization, first-order phase transitions, ergodicity breaking, and mapping to a 1D Ising model, with implications for experimental verification.

Contribution

It provides the first detailed analysis of dipolar needles in the microcanonical ensemble, demonstrating spontaneous magnetization, phase transition characteristics, and ergodicity breaking with an analytical model.

Findings

Spontaneous magnetization observed in finite cubic lattices.

First-order phase transition from paramagnetic to ferromagnetic phase.

Evidence of ergodicity breaking and magnetization gaps.

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 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.