Abstract
The double hexagonal lattice model is a new statistical model constructed by connecting two-dimensional hexagonal structured materials such as Graphene and Lie symmetries. The double hexagonal structure of this model appears in the G2 symmetry of Lie algebras. To investigate the magnetic properties of this new lattice model, an Ising-1/2 model was constructed with spin values σ = ±1. An effective-field theory (EFT) method was used with the differential operator technique to formulate the identity of the spin system, based on Callen's work. Different phase diagrams were established by varying the double-exchange interaction couplings and the super-exchange interaction coupling present in the model. The accurate results obtained by the EFT method were compared with those found by the mean-field approximation (MFA) method. The symmetry of the MFA diagrams was broken in the EFT diagrams. The critical temperature behavior was found to depend on the type of super-exchange ferromagnetism.
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