Ground states, residual entropies, and specific heat capacity properties of frustrated Ising system on pyrochlore lattice in effective field theory cluster approximations

The thermodynamics of the antiferromagnetic spin-1∕2 Ising model in the presence of the external magnetic field on the geometrically frustrated pyrochlore lattice is investigated using various effective field theory cluster approximations up to the cluster size consisting of 7 sites in the form of two site-connected elementary tetrahedrons. The system of all ground states of the model is determined and the dependence of the magnetization, of the specific heat capacity, as well as of the entropy of the model on the used cluster approximation is investigated. It is shown that the thermodynamic properties of the ground states depend on the used cluster approximation and tend to those obtained in the framework of other theoretical approaches with the increasing of the cluster size. The analysis shows that, although it seems that the EFT cluster approximation represents quite effective approach for the investigation of properties of the model for some specific intervals and discrete values of the external magnetic field, in general, one must be very careful when interpreting obtained results. The dependence of the critical temperature, of the spontaneous magnetization, as well as of the specific heat capacity of the ferromagnetic model on the used cluster approximation is also discussed.