An Ising model on a 3D honeycomb zigzag-ladder lattice: a solution to the ground-state problem and application to the SrRE$_2$O$_4$ and BaRE$_2$O$_4$ magnets

An exact solution (incomplete) of the ground-state problem for an Ising model in an external field on a 3D honeycomb zigzag-ladder lattice with two types of sites is found. It is shown that the geometrical frustration due to the presence of triangle elements leads to the emergence of a variety of magnetic phases. The majority of these are partially disordered (highly degenerate). The theoretical results are used to explain the sequence of experimentally observed phase transitions in the honeycomb zigzag-ladder magnets and to predict the appearance of new phases.

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