Phase transition for the Ising model with mixed spins on a Cayley tree. (1st May 2022)

• Record Type: Journal Article
• Authors: Akin, Hasan; Mukhamedov, Farrukh
• Is Part Of: Journal of statistical mechanics. (2022:May)
• Publication Date: 2022-05-01
• Subjects: classical phase transitions; Statistical mechanics -- Periodicals; Mechanics -- Statistical methods -- Periodicals; 530.1305
• DOI: 10.1088/1742-5468/ac68e4
• Languages: English
• ISSNs: 1742-5468

Abstract

Abstract: In the present paper, we consider the Ising model with mixed spin- (1, 1/2) on the second order Cayley tree. For this model, a construction of splitting Gibbs measures is given that allows us to establish the existence of the phase transition (non-uniqueness of Gibbs measures). We point out that, in the phase transition region, the considered model exhibits three translation-invariant Gibbs measures in the ferromagnetic and anti-ferromagnetic regimes, respectively, while the classical Ising model does not possess such Gibbs measures in the anti-ferromagnetic setting. It turns out, that like the classical Ising model, we can find a disordered Gibbs measure, therefore, its non-extremity and extremity are investigated by means of tree-indexed Markov chains.