Extremality of Disordered Phase of λ-Model on Cayley Trees

In this paper, we consider the λ-model for an arbitrary-order Cayley tree that has a disordered phase. Such a phase corresponds to a splitting Gibbs measure with free boundary conditions. In communication theory, such a measure appears naturally, and its extremality is related to the solvability of...

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Bibliographic Details
Published in:Algorithms 2022-01, Vol.15 (1), p.18
Main Author: Mukhamedov, Farrukh
Format: Article
Language:English
Subjects:
Boundary conditions
Cayley tree
Communication theory
extramality
Free boundaries
Phase transitions
splitting Gibbs measure
Statistical physics
Temperature
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Summary:In this paper, we consider the λ-model for an arbitrary-order Cayley tree that has a disordered phase. Such a phase corresponds to a splitting Gibbs measure with free boundary conditions. In communication theory, such a measure appears naturally, and its extremality is related to the solvability of the non-reconstruction problem. In general, the disordered phase is not extreme; hence, it is natural to find a condition for their extremality. In the present paper, we present certain conditions for the extremality of the disordered phase of the λ-model.
ISSN:1999-4893
1999-4893
DOI:10.3390/a15010018