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

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• 作者：Mukhamedov ; Farruh
• 关键词：47A67 ; 47L90 ; 47N55 ; 82B20 ; von Neumann algebra ; λ ; -model ; Cayley tree ; unordered phase ; Gibbs measure ; GNS construction
• 刊名：Reports on Mathematical Physics
• 出版年：2004
• 出版时间：February, 2004
• 年：2004
• 卷：53
• 期：1
• 页码：1-18
• 全文大小：797 K

文摘

In this paper we consider nearest-neighbours models, where the spin takes values in the set Φ = {η₁, η₁, …, 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.