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.

反铁磁自旋的热力学$\mathrm{1个}∕2$使用各种有效的场论簇近似方法，研究了几何受阻的烧绿石晶格上存在外部磁场时的伊辛模型，该簇近似值包括由两个以位点连接的基本四面体形式的7个位点组成的簇大小。确定了模型所有基态的系统，并研究了磁化强度，比热容量以及模型的熵对所使用的簇近似的依赖性。结果表明，随着团簇尺寸的增加，基态的热力学性质取决于所使用的团簇近似，并且趋于于在其他理论方法的框架内获得的那些。分析表明，尽管对于某些特定间隔和外部磁场的离散值，EFT簇近似似乎是研究模型属性的有效方法，但通常在解释获得的结果时必须非常小心。还讨论了临界温度，自发磁化强度以及铁磁模型的比热容对所使用的簇近似的依赖性。