  Some strongly frustrated magnets such as the "spin-ice" compounds fail to
produce any magnetic order at finite temperatures even in the presence of
magnetic field. Still they have very unusual low-temperature thermodynamic
properties related to the field-induced ground state transitions. Here we show
that general qualitative picture of such peculiar thermodynamics can be
obtained in the antiferromagnetic Ising model on the triangular Husimi lattice.
The analytical results for this model show magnetic plateaus, entropy spikes,
crossing points and peculiarities in magnetic susceptibility and specific heat
behavior reflecting the existence of ground state transitions. These signatures
of strong frustration may help in search of new frustrated magnets and in the
interpretation of experimental data.
