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

Hasan Akın

Chaos, Solitons & Fractals, 2024, vol. 189, issue P2

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.

Keywords: Ising model with mixed spin-(s, 1/2); Disordered phase; Gibbs measure; Phase transition; Kesten–Stigum condition (search for similar items in EconPapers)
Date: 2024
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:189:y:2024:i:p2:s0960077924012852

DOI: 10.1016/j.chaos.2024.115733

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