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We perform Monte Carlo simulations to study the relaxation of single-domain nanoparticles that are located on a simple cubic lattice with anisotropy axes pointing in the z-direction, under the combined influence of anisotropy energy, dipolar interaction and ferromagnetic interaction of strength J . We compare the results of classical Heisenberg systems with three-dimensional magnetic moments μ i to those of Ising systems and find that Heisenberg systems show a much richer and more complex dynamical behavior. In contrast to Heisenberg systems, Ising systems need large activation energies to turn a spin and also possess a smaller configuration space for the orientation of the μ i . Accordingly, Heisenberg systems possess a whole landscape of different states with very close-lying energies, while Ising systems tend to get frozen in one random state far away from the ground state. For Heisenberg systems, we identify two phase transitions: (i) at intermediate J between domain and layered states and (ii) at larger J between layered and ferromagnetic states. Between these two transitions, the layered states change their appearance and develop a sub-structure, where the orientation of the μ i in each layer depends on J , so that for each value of J , a new ground state appears.

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