Exact description of paramagnetic and ferromagnetic phases of an Ising model on a third-order Cayley tree

2017/08/07 by Hasan Akın, Hasan Akin, Akin, Hasan
Mathematics · Physics and Astronomy · #05.70.Ce #05.70.Fh #75.10.Hk #Complex Network Analysis Techniques #FOS: Physical sciences #Mathematical Physics (math-ph) #Statistical Mechanics (cond-mat.stat-mech) #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #cond-mat.stat-mech #math-ph #math.MP #msc:05.70.Ce #msc:05.70.Fh #msc:75.10.Hk

paper · pdf · doi:10.48550/arxiv.1708.02585

16 pages, 6 figures

arxiv created 2017/08/07 · openalex publication_date 2017/08/07 · arxiv updated 2017/08/09 · openalex created_date 2017/08/17 · openalex updated_date 2026/07/28

Abstract

In this paper we analytically study the recurrence equations of an Ising model with three competing interactions on a Cayley tree of order three. We exactly describe paramagnetic and ferromagnetic phases of the Ising model. We obtain some rigorous results: critical temperatures and curves, number of phases, partition function. Ganikhodjaev et al. [J. Concrete and Applicable Mathematics, 9 (1), 26-34 (2011)] have numerically studied the Ising model on a second-order Cayley tree. We compare the numerical results to exact solutions of mentioned model.

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