Factors Generated by XY-Model with Competing Ising Interactions on the Cayley Tree

Farrukh Mukhamedov; Soueidy El Gheteb

doi:10.1007/s00023-019-00853-9

Factors Generated by XY-Model with Competing Ising Interactions on the Cayley Tree

Farrukh Mukhamedov
, Soueidy El Gheteb

Department of Mathematical Sciences

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

10 Citations (Scopus)

Abstract

In the present paper, we consider a quantum Markov chain corresponding to the XY-model with competing Ising interactions on the Cayley tree of order two. Earlier, it was proved that this state does exist and is unique. Moreover, it has clustering property. This means that the von Neumann algebra generated by this state is a factor. In the present paper, we establish that the factor generated by this state may have type III _λλ∈ (0 , 1) which is unusual for states associated with models with nontrivial interactions.

Original language	English
Pages (from-to)	241-253
Number of pages	13
Journal	Annales Henri Poincare
Volume	21
Issue number	1
DOIs	https://doi.org/10.1007/s00023-019-00853-9
Publication status	Published - Jan 1 2020

ASJC Scopus subject areas

Statistical and Nonlinear Physics
Nuclear and High Energy Physics
Mathematical Physics

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abstract = "In the present paper, we consider a quantum Markov chain corresponding to the XY-model with competing Ising interactions on the Cayley tree of order two. Earlier, it was proved that this state does exist and is unique. Moreover, it has clustering property. This means that the von Neumann algebra generated by this state is a factor. In the present paper, we establish that the factor generated by this state may have type III λλ∈ (0 , 1) which is unusual for states associated with models with nontrivial interactions.",

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Factors Generated by XY-Model with Competing Ising Interactions on the Cayley Tree

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