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New disordered phases of the (s,1/2)-mixed spin Ising model for arbitrary spin s

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  • Akın, Hasan

Abstract

In this paper, we introduce an Ising model with mixed spin (s,1/2) (abbreviated as (s,1/2)-MSIM) for any spin set [−s,s]∩Z on a semi-infinite second-order Cayley tree and construct translation-invariant splitting Gibbs measures (TISGMs) associated with the model. We prove that as the weight of the s-spin value increases, the repelling region of the fixed point ℓ0(s), corresponding to the TISGM, expands, leading to a broadening of the phase transition region. We also study tree-indexed Markov chains associated with the (s,1/2)-MSIM. Additionally, we clarify the extremality of the associated disordered phases by utilizing the method of Martinelli, Sinclair, and Weitz (Martinelli et al., 2007). By examining the non-extremality of the disordered phases related to the (s,1/2)-MSIM on the Cayley tree using the Kesten–Stigum condition, we extend previous research findings to encompass any set of spins in [−s,s]∩Z. Furthermore, we prove that as the weight of the s-spin value increases, the region where the disordered phase corresponding to the (s,1/2)-MSIM is extreme narrows, while the region where it is non-extreme widens.

Suggested Citation

  • Akın, Hasan, 2024. "New disordered phases of the (s,1/2)-mixed spin Ising model for arbitrary spin s," Chaos, Solitons & Fractals, Elsevier, vol. 189(P2).
    • Handle: RePEc:eee:chsofr:v:189:y:2024:i:p2:s0960077924012852
    DOI: 10.1016/j.chaos.2024.115733
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    References listed on IDEAS

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    1. Ostilli, M., 2012. "Cayley Trees and Bethe Lattices: A concise analysis for mathematicians and physicists," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(12), pages 3417-3423.
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