Ising model on the semi-infinite Cayley tree of third order with inhomogeneous interactions

• Main Authors: Ganikhodjaev, Nasir, Ibrahim, Huda Husna
• Format: Article
• Language: English; English; English
• Published: American Institute of Physics Inc. 2018
• Subjects: QA Mathematics
• Online Access: http://irep.iium.edu.my/58331/3/Presentation%20SKSM25_NG.pdf; http://irep.iium.edu.my/58331/18/58331_Ising%20model%20on%20the%20semi-infinite%20Cayley%20tree.pdf; http://irep.iium.edu.my/58331/19/58331_Ising%20model%20on%20the%20semi-infinite%20Cayley%20tree_SCOPUS.pdf; http://irep.iium.edu.my/58331/; https://aip.scitation.org/doi/pdf/10.1063/1.5041657?class=pdf

In this paper we investigate the problem of phase transition for Ising model on a semi-infinite Cayley tree of third order with inhomogeneous left, middle and right parameters describing the strength of the interactions between left, middle and right nearest-neighbors respectively. We produce a recurrent equation that describes a limit behavior of the sequence conditional Gibbs measures and prove that if at least two of the parameters are positive one can reach phase transition.