Title: Gibbs measures of an Ising model with competing interactions on the triangular chandelier-lattice
Author(s):

H. Akιn (Ceyhun Atuf Kansu Caddesi 1164. Sokak, 9/4, TR06105, Çankaya, Ankara, Turkey)

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

Key words: chandelier lattices, Gibbs measures, Ising model, phase transition
PACS: 05.70.Fh, 05.70.Ce, 75.10.Hk

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