Lyapunov operator \mathcal L with degenerate kernel and Gibbs measures

2017/08/23 by Yu. Kh. Èshkabilov, Yu. Kh. Eshkabilov, Eshkabilov, Yu. Kh. +2
Mathematics · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #FOS: Mathematics #Functional Analysis (math.FA) #Mathematical Dynamics and Fractals #Theoretical and Computational Physics #math.FA

paper · pdf · doi:10.48550/arxiv.1708.06903

arXiv admin note: text overlap with arXiv:1509.04883

arxiv created 2017/08/23 · openalex publication_date 2017/08/23 · arxiv updated 2017/08/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we'll give a connection between four competing interactions (external field, nearest neighbor, second neighbors and triples of neighbors) of models with uncountable (i.e. [0,1]) set of spin values on the Cayley tree of order two and Lyapunov integral equation. Also we'll study fixed points of Lyapunov operator with degenerate kernel which each fixed point of the operator is correspond to a \it translation-invariant Gibbs measure.

Citations

• Four Competing interactions for models with uncountable set of spin values on a Cayley Tree

Related

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• Four Competing interactions for models with uncountable set of spin values on a Cayley Tree
• Non-translation-invariant Gibbs Measures for Models With Uncountable Set of Spin Values on a Cayley Tree
• Phase Transitions for a model with uncountable set of spin values on a Cayley tree
• Positive fixed points of Hammerstein's integral operators with degenerate kernel