scholarly journals A quantum Markov chain approach to phase transitions for quantum Ising model with competing XY-interactions on a Cayley tree

2020 ◽  
Vol 61 (9) ◽  
pp. 093505
Author(s):  
Farrukh Mukhamedov ◽  
Abdessatar Barhoumi ◽  
Abdessatar Souissi ◽  
Soueidy El Gheteb
Keyword(s):  
Markov Chain ◽  
Phase Transitions ◽  
Ising Model ◽  
Cayley Tree ◽  
Quantum Markov Chain ◽  
Markov Chain Approach ◽  
Quantum Ising Model

Uniqueness of Quantum Markov Chain Associated with XY-Ising Model on Cayley Tree of Order Two

2017 ◽  
Vol 24 (02) ◽  
pp. 1750010 ◽  
Author(s):  
Farrukh Mukhamedov ◽  
Soueidy El Gheteb
Keyword(s):  
Markov Chain ◽  
Ising Model ◽  
Markov Chains ◽  
Boundary Conditions ◽  
Finite Volume ◽  
Cayley Tree ◽  
Limit State ◽  
Weak Limit ◽  
Quantum Markov Chain ◽  
Quantum Markov Chains

In this paper, we consider backward and forward Quantum Markov Chains (QMC) associated with XY -Ising model on the Cayley tree of order two. We construct finite volume states with boundary conditions, and define QMC as a weak limit of those states which depend on the boundary conditions. We prove that the limit state is a unique QMC associated with such a model, this means the QMC does not depend on the boundary conditions. Moreover, we observe the relation between backward and forward QMC.

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