Entropic selection of magnetization in a frustrated two-dimensional magnetic model

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 ${J}_{1}$ (intracluster couplings) and ${J}_{2}$ (intercluster 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 nontrivial. This model is a first step towards modeling properties of a class of frustrated magnetic structures composed of coupled spin clusters.