Influence of dilution on magnetization properties of geometrically frustrated magnetic systems: Effective-field theory cluster approximations on kagome lattice

The influence of the site dilution on the magnetization properties of the antiferromagnetic spin-1/2 Ising model on the kagome lattice is systematically investigated using various n-site cluster effective-field theory approximations up to the cluster size $n=12$. It is shown that, regardless of the cluster approximation, the site dilution of the system leads, in addition to the existence of the standard saturated ground state, to the formation of four nontrivial plateau ground states together with five single-point ground states that separate them in the zero temperature limit. It is also shown that, while magnetization properties of the saturated ground state and two single-point ground states are stable with respect to the used cluster approximation, the magnetization properties of all four nontrivial plateau ground states and three single-point ground states that separate them strongly depend on the used approximation and have tendency to approach each other with increasing of the cluster approximation.