Abstract Geometrically frustrated spin models with competing interaction parameters and the phase diagram of their corresponding T = 0 ground state energies are studied. The partition function defined by means of the transfer matrix method is calculated and the thermodynamical properties of the diamond Ising model are discussed. A more complete picture, including magnetic properties, is provided by the frustrated Ising model, in which an external magnetic field is included. Using the general transfer matrix procedure we calculate all correlation functions related to these three unitary cells in the proposed model. It is worthwhile to remark that the existence of a spatial symmetry between these unitary cells allows the correlation functions to be written in a very simple form.