Frustrated Magnetism in the Quantum Ising Model on the Swedenborgite Lattice
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In selected lattice systems, it is impossible to satisfy all the antiferromagnetic interactions between the spins simultaneously. Due to this frustration the degeneracy of the ground state becomes very large, often scaling with the size of the system. An antiferromagnetic model of Ising spins with on the three-dimensional Swedenborgite lattice will similarly be frustrated and will behave like a spin liquid in all parameter regimes. Fluctuations, which may be either thermal or quantum-mechanical in nature, between the states in the large (disordered) ground state manifold may be biased towards one of them. This causes the system to select a unique (ordered) ground state, in an effect called order-by-disorder. Our objective is now to investigate the effects of quantum fluctuations on the ground states of the Swedenborgite Ising model and to examine it for potential order-by-disorder effects. This will ultimately result in the construction of a tentative phase diagram of this system.