Applicability of effective field theory cluster approximations for investigation of geometrically frustrated magnetic systems: Antiferromagnetic model on kagome lattice

We investigate the antiferromagnetic spin-1∕2 Ising model in the presence of the external magnetic field on the geometrically frustrated kagome lattice using the effective field theory cluster approximation up to the size of the cluster consisting of 12 connected sites which form typical basic geometrical structure of the kagome lattice. The magnetization properties, systems of the ground states, as well as the specific heat capacity behavior of the model are investigated depending on the cluster size. It is shown that properties of the model related to the frustration, such as the formation of discrete system of ground states, strongly depend on the used cluster approximation. It is shown that besides physically relevant ground states the model also exhibits the existence of ground states which are related to the used effective field theory technique and should disappear in the limit n→∞ of the n-site cluster approximation with simultaneous formation of physically relevant ground states of the Ising model on the kagome lattice. The unphysical origin of these ground states is also demonstrated by the low temperature behavior of the specific heat capacity which exhibits even inverse Schottky peaks with negative values of the specific heat capacity which are reduced with increasing of the cluster size approximation towards physically acceptable behavior. For completeness, the dependence of the position of the critical temperature and the behavior of the spontaneous magnetization and specific heat capacity of the ferromagnetic model in the zero external magnetic field on the size of the cluster approximation is also briefly discussed.