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In this paper, we consider an Ising model with three competing interactionson a triangular chandelier-lattice (TCL). We describe the existence,uniqueness, and non-uniqueness of translation-invariant Gibbs measuresassociated with the Ising model. We obtain an explicit formula for Gibbsmeasures with a memory of length 2 satisfying consistency conditions. It isrigorously proved that the model exhibits phase transitions only for givenvalues of the coupling constants. As a consequence of our approach, thedichotomy between alternative solutions of Hamiltonian models on TCLs issolved. Finally, two numerical examples are given to illustrate the usefulnessand effectiveness of the proposed theoretical results.

Gibbs measures of an Ising model with competing interactions on the triangular chandelier-lattice