  We introduce a simple lattice model with Ising spins to explain recent
experimental results on spin freezing in a hollandite-type structure. We argue
that geometrical frustration of the lattice in combination with
nearest-neighbour antiferromagnetic (AFM) interactions is responsible for the
appearance of a spin-glass phase in presence of disorder. We investigate this
system numerically using parallel tempering. The model reproduces the magnetic
behaviour of oxides with hollandite structure, such as $\alpha-\text{MnO}_2$
and presents a rich phenomenology: in absence of disorder three types of ground
states are possible, depending on the relative strength of the interactions,
namely AFM ordered and two different disordered, macroscopically degenerate
families of ground states. Remarkably, for sets of AFM couplings having an AFM
ground state in the clean system, there exists a critical value of the disorder
for which the ground state is replaced by a spin-glass phase while maintaining
all couplings AFM. To the best of our knowledge this is the only existing model
that presents this kind of transition with short-range AFM interactions. We
argue that this model could be useful to understand the relation between AFM
coupling, disorder and the appearance of a spin-glass phase.
