On a factor associated with the unordered phase of λ-model on a Cayley tree

Farruh Mukhamedov

doi:10.1016/S0034-4877(04)90001-8

On a factor associated with the unordered phase of λ-model on a Cayley tree

Farruh Mukhamedov

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

32 Citations (Scopus)

Abstract

In this paper we consider nearest-neighbours models, where the spin takes values in the set Φ = {η₁, η ₂, ..., η_q} and is assigned to the vertices of the Cayley tree Γ^k. The Hamiltonian is defined by some given λ-function. We find a condition for the function λ to determine a type of von Neumann algebra generated by the GNS construction associated with the unordered phase of the λ-model. We give also some physical applications of the obtained result.

Original language	English
Pages (from-to)	1-18
Number of pages	18
Journal	Reports on Mathematical Physics
Volume	53
Issue number	1
DOIs	https://doi.org/10.1016/S0034-4877(04)90001-8
Publication status	Published - Feb 2004
Externally published	Yes

Keywords

Cayley tree
GNS construction
Gibbs measure
Unordered phase
von Neumann algebra
λ-model

ASJC Scopus subject areas

Statistical and Nonlinear Physics
Mathematical Physics

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10.1016/S0034-4877(04)90001-8

Cite this

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AB - In this paper we consider nearest-neighbours models, where the spin takes values in the set Φ = {η1, η 2, ..., ηq} and is assigned to the vertices of the Cayley tree Γk. The Hamiltonian is defined by some given λ-function. We find a condition for the function λ to determine a type of von Neumann algebra generated by the GNS construction associated with the unordered phase of the λ-model. We give also some physical applications of the obtained result.

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KW - GNS construction

KW - Gibbs measure

KW - Unordered phase

KW - von Neumann algebra

KW - λ-model

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JO - Reports on Mathematical Physics

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On a factor associated with the unordered phase of λ-model on a Cayley tree

Abstract

Keywords

ASJC Scopus subject areas

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