Author:
Akin Hasan,Mukhamedov Farrukh
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.
Subject
Statistics, Probability and Uncertainty,Statistics and Probability,Statistical and Nonlinear Physics
Reference30 articles.
1. A novel computational method of the free energy for an Ising model on Cayley tree of order three;Akın;Chin. J. Phys.
2. The study of mixed spin-1 and spin-1/2: entropy and isothermal entropy change;Albayrak;Physica A,2020
3. Extremity of the disordered phase in the Ising model on the Bethe lattice;Bleher;Commun. Math. Phys.,1990
4. Mixed-spin Ising model on the Bethe lattice;da Silva;Phys. Rev. B,1991
Cited by
14 articles.
订阅此论文施引文献
订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献