On Quantum Markov Chains on Cayley Tree III: Ising Model

Luigi Accardi; Farrukh Mukhamedov; Mansoor Saburov

doi:10.1007/s10955-014-1083-y

On Quantum Markov Chains on Cayley Tree III: Ising Model

Luigi Accardi, Farrukh Mukhamedov, Mansoor Saburov

Research output: Contribution to journal › Article › peer-review

15 Citations (Scopus)

Abstract

In this paper, we consider the classical Ising model on the Cayley tree of order k, (k ≥ 2) and show 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 the classical critical temperature.

Original language	English
Pages (from-to)	303-329
Number of pages	27
Journal	Journal of Statistical Physics
Volume	157
Issue number	2
DOIs	https://doi.org/10.1007/s10955-014-1083-y
Publication status	Published - Oct 2014
Externally published	Yes

Keywords

Cayley tree
Ising model
Phase transition
Quantum Markov chain

ASJC Scopus subject areas

Statistical and Nonlinear Physics
Mathematical Physics

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10.1007/s10955-014-1083-y

Cite this

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abstract = "In this paper, we consider the classical Ising model on the Cayley tree of order k, (k ≥ 2) and show 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 the classical critical temperature.",

keywords = "Cayley tree, Ising model, Phase transition, Quantum Markov chain",

author = "Luigi Accardi and Farrukh Mukhamedov and Mansoor Saburov",

note = "Publisher Copyright: {\textcopyright} 2014, Springer Science+Business Media New York.",

year = "2014",

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AU - Mukhamedov, Farrukh

AU - Saburov, Mansoor

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Y1 - 2014/10

N2 - In this paper, we consider the classical Ising model on the Cayley tree of order k, (k ≥ 2) and show 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 the classical critical temperature.

AB - In this paper, we consider the classical Ising model on the Cayley tree of order k, (k ≥ 2) and show 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 the classical critical temperature.

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KW - Ising model

KW - Phase transition

KW - Quantum Markov chain

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On Quantum Markov Chains on Cayley Tree III: Ising Model

Abstract

Keywords

ASJC Scopus subject areas

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