An effective-field theory study of trilayer Ising nanostructure: Thermodynamic and magnetic properties

•Correlation identities for the Ising model on a nanostructure of hexagonal lattices are obtained.•From the spin correlation identities the effective-field theory is applied.•Lines of phase transitions continuous are obtained.•The critical temperature and the compensation temperature are investigated.•The free energy, the internal energy, the entropy and the specific heat were obtained. Thermodynamic and magnetic properties of a trilayer nanostructure of hexagonal lattices described by the spin-1/2 Ising model are investigated by the use of the effective-field theory (EFT) with correlations. The results for the magnetization, the free energy, the internal energy, the entropy, the specific heat and the critical frontiers were obtained. The critical temperature and the compensation temperature are investigated with a negative interlayer coupling, in order to clarify the distinction between the ferromagnetic and ferrimagnetic behaviors. From the thermal variations of the total magnetization, the six compensation types can be found, i.e., L-, Q-, R-, S-, P-, and N-types.