Effective field theory in larger clusters – Ising model

•General formulation for effective field theory in finite clusters obtained.•The advantages and disadvantages of the method discussed.•Application of the formulation to the 2D and 3D lattices performed.

General formulation for the effective field theory with differential operator technique and the decoupling approximation with larger finite clusters (namely EFT-N formulation) has been derived for several S-1/2 bulk systems. The effect of enlarging this finite cluster on the results for the critical temperatures and thermodynamic properties has been investigated in detail. Beside the improvement on the critical temperatures, the necessity of using larger clusters, especially in nanomaterials has been discussed. Using the derived formulation, applications on the effective field and mean field renormalization group techniques have also been performed.