Geodesic
Pinned gradient measures of SOS model associated with $H_A$-boundary laws on Cayley trees
Nanosistemy: fizika, himiâ, matematika, Tome 16 (2025) no. 2, pp. 154-163

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This paper investigates pinned gradient measures for SOS (Solid-On-Solid) models associated with $H_A$-boundary laws of period two, a class that encompasses all 2-height periodic gradient Gibbs measures corresponding to a spatially homogeneous boundary law. While previous research has predominantly focused on a spatially homogeneous boundary law and corresponding GGMs on Cayley trees, this study extends the analysis by providing a comprehensive characterization of such measures. Specifically, it demonstrates the existence of pinned gradient measures on a set of $G$-admissible configurations and precisely quantifies their number under certain temperature conditions.
Keywords: SOS model, spin values, Cayley tree, gradient measure, gradient Gibbs measure, two periodic boundary law.
Mots-clés : gradient configuration, $G$-admissible configuration 
@article{NANO_2025_16_2_a3,
     author = {Farhod H. Haydarov and Risolat A. Ilyasova and Khudoyor S. Mamayusupov},
     title = {Pinned gradient measures of {SOS} model associated with $H_A$-boundary laws on {Cayley} trees},
     journal = {Nanosistemy: fizika, himi\^a, matematika},
     pages = {154--163},
     publisher = {mathdoc},
     volume = {16},
     number = {2},
     year = {2025},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/NANO_2025_16_2_a3/}
}
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Farhod H. Haydarov; Risolat A. Ilyasova; Khudoyor S. Mamayusupov. Pinned gradient measures of SOS model associated with $H_A$-boundary laws on Cayley trees. Nanosistemy: fizika, himiâ, matematika, Tome 16 (2025) no. 2, pp. 154-163. http://geodesic.mathdoc.fr/item/NANO_2025_16_2_a3/