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We discuss the magnetic ground state and properties of a frustrated two-dimensional classical Heisenberg model of interacting hexagonal clusters of spins. The energy of the ground states is found exactly for arbitrary values of J₁ (intra-cluster couplings) and J₂ (inter-cluster couplings). Our main results concern a frustrated region of the phase diagram, where we show that the set of ground states has a degeneracy larger than that due to global rotation symmetry. Furthermore, the ground state manifold does not have a fixed total magnetization~: there is a range of allowed values. At finite temperature, our Monte-Carlo simulations show that the entropy selects the most probable value of the total magnetization, while the histogram of the Monte-Carlo time series is non-trivial. This model is a first step towards modelling properties of a class of frustrated magnetic structures composed of coupled spin clusters.
Jagannathan et al. (Thu,) studied this question.