Types of factors generated by quantum Markov states of Ising model with competing interactions on the Cayley tree

In this paper, we consider Quantum Markov States (QMS) corresponding to the Ising model with competing interactions on the Cayley tree of order two. Earlier, some algebraic properties of these states were investigated. In this paper, we prove that if the competing interaction is rational then the von Neumann algebra, corresponding to the QMS associated with disordered phase of the model, has type [Formula: see text], [Formula: see text].

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On an Algebraic Property of the Disordered Phase of the Ising Model with Competing Interactions on a Cayley Tree

Mathematical Physics Analysis and Geometry ◽

10.1007/s11040-016-9225-x ◽

2016 ◽

Vol 19 (4) ◽

Cited By ~ 8

Author(s):

Farrukh Mukhamedov ◽

Abdessatar Barhoumi ◽

Abdessatar Souissi

Keyword(s):

Ising Model ◽

Cayley Tree ◽

Algebraic Property ◽

Competing Interactions ◽

Disordered Phase

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Ising model on the Cayley tree with competing interactions up to the third Nearest-neighbors with spins belonging to different branches of the tree

Journal of the Korean Physical Society ◽

10.3938/jkps.66.1200 ◽

2015 ◽

Vol 66 (8) ◽

pp. 1200-1206 ◽

Cited By ~ 5

Author(s):

Nasir Ganikhodjaev ◽

Mohd Hirzie Mohd Rodzhan

Keyword(s):

Ising Model ◽

Cayley Tree ◽

Nearest Neighbors ◽

Competing Interactions ◽

The Third

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Low-temperature antiferromagnetism of Ising model with competing interactions

ВЕСТНИК ПЕРМСКОГО УНИВЕРСИТЕТА ФИЗИКА ◽

10.17072/1994-3598-2021-2-64-71 ◽

2021 ◽

pp. 64-71

Author(s):

Kirill Tsiberkin ◽

Keyword(s):

Ising Model ◽

Low Temperature ◽

Temperature Shift ◽

Second Order ◽

Square Lattice ◽

Antiferromagnetic Coupling ◽

Competing Interactions ◽

Saturation State ◽

Spin Configuration ◽

Competing Interaction

The paper presents a numerical analysis of equilibrium state and spin configuration of square lattice Ising model with competing interaction. The most detailed description is given for case of ferromagnetic interaction of the first-order neighbours and antiferromagnetic coupling of the second-order neighbours. The numerical method is based on Metropolis algorithm. It uses 128×128 lattice with periodic boundary conditions. At first, the simulation results show that the system is in saturation state at low temperatures, and it turns into paramagnetic state at the Curie point. The competing second-order interaction makes possible the domain structure realization. This state is metastable, because its energy is higher than saturation energy. The domains are small at low temperature, and their size increases when temperature is growing until the single domain occupies the whole simulation area. In addition, the antiferromagnetic coupling of the second-order neighbours reduces the Curie temperature of the system. If it is large enough, the lattice has no saturation state. It turns directly from the domain state into paramagnetic phase. There are no extra phases when the system is antiferromagnetic in main order, and only the Neel temperature shift realizes here.

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