Quantum phase transition for Ising type models on a Cayley tree of order two

Mukhamedov, Farrukh and Barhoumi, Abdessatar and Soussi, Abdessatar (2014) Quantum phase transition for Ising type models on a Cayley tree of order two. In: 35th International Conference on Quantum Probability and Related Topics (QP35), 22-26 August 2014, Korea.

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Abstract

In this work, we construct a quantum Markov chain (QMC) associated by the classical Ising model with competing interactions on the Cayley tree of order two. In the construction QMC is defined as a weak limit of finite volume states on quasi-local algebras with boundary conditions. We point out that phase transitions in a quantum setting play an important role to understand quantum spin systems We have defined a notion of phase transition in QMC scheme. Namely, such a notion is based on the quasi-equivalence of QMC. Therefore, such a phase transition is purely non-commutative. In this work we establish the existence of the phase transition in the following sense: there exists two quantum Markov states which are not quasi-equivalent. It turns out that the found critical temperature coincides with usual critical temperature.

Item Type:	Conference or Workshop Item (Lecture)
Additional Information:	5537/38019
Uncontrolled Keywords:	Quantum phase transition
Subjects:	Q Science > QA Mathematics
Kulliyyahs/Centres/Divisions/Institutes (Can select more than one option. Press CONTROL button):	Kulliyyah of Science > Department of Computational and Theoretical Sciences
Depositing User:	Dr. Farrukh Mukhamedov
Date Deposited:	17 Sep 2014 14:32
Last Modified:	19 Jun 2018 10:38
URI:	http://irep.iium.edu.my/id/eprint/38019

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