  Thermodynamic and magnetocaloric properties of geometrically frustrated Ising
spin clusters of selected shapes and sizes are studied by exact enumeration. In
the ground state the magnetization and the entropy show step-wise variations
with an applied magnetic field. The number of steps, their widths and heights
depend on the cluster shape and size. While the character of the magnetization
plateau heights is always increasing, the entropy is not necessarily decreasing
function of the field, as one would expect. For selected clusters showing some
interesting ground-state properties, the calculations are extended to finite
temperatures by exact enumeration of densities of states in the
energy-magnetization space. In zero field the focus is laid on a peculiar
behavior of some thermodynamic quantities, such as the entropy, the specific
heat and the magnetic susceptibility. In finite fields various thermodynamic
functions are studied in the temperature-field parameter plane and particular
attention is paid to the cases showing an enhanced magnetocaloric effect. The
exact results on the finite clusters are compared with the thermodynamic limit
behavior obtained from Monte Carlo simulations.
