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THE EXTREMALITY OF DISORDERED PHASES FOR THE MIXED SPIN-(1,1/2) ISING MODEL ON CAYLEY TREE OF ARBITRARY ORDER
  • HASAN AKIN,
  • Farrukh Mukhamedov
HASAN AKIN
Abdus Salam International Centre for Theoretical Physics

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Farrukh Mukhamedov
UAE University College of Science
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Abstract

The aim of this paper is to continue the investigation into the set of translation-invariant splitting Gibbs measures (TISGMs) for Ising model having the mixed spin (1,1/2) (shortly, (1,1/2)-MSIM) on a Cayley tree of arbitrary order. In our previous work [Akın and Mukhamedov, J. Stat. Mech. (2022) 053204], we provided a thorough explanation of the TISGMs, and studied the extremality of disordered phases using a Markov chain with a tree index on a semi-finite Cayley tree with order two. In this paper, we construct the TISGMs and tree-indexed Markov chains associated with to the model. Considering a tree-indexed Markov chain on a Cayley tree of any order, we clarify the extremality of the related disordered phases. By using the Kesten-Stigum condition (KSC), we investigate non-extremality of the disordered phases by means of the eigenvalues of the stochastic matrix associated with (1,1/2)-MSIM on a CT of order k≥2.