Pinned gradient measures of SOS model associated with HA-boundary laws on Cayley trees
https://doi.org/10.17586/2220-8054-2025-16-2-154-163
Abstract
This paper investigates pinned gradient measures for SOS (Solid-On-Solid) models associated with HA-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,
gradient configuration,
G-admissible configuration,
spin values,
Cayley tree,
gradient measure,
gradient Gibbs measure,
two periodic boundary law
Supporting agencies: We sincerely thank the referee for their valuable and insightful comments, which have helped improve this work.
About the Authors
F. H. Haydarov
V. I. Romanovskiy Institute of Mathematics, Uzbekistan Academy of Sciences; New Uzbekistan University
Uzbekistan
Uzbekistan
Farhod H. Haydarov
9, University str., Tashkent, 100174
54, Mustaqillik Ave., Tashkent, 100007
R. A. Ilyasova
New Uzbekistan University; National University of Uzbekistan
Uzbekistan
Uzbekistan
Risolat A. Ilyasova
54, Mustaqillik Ave., Tashkent, 100007
University str., 4 Olmazor district, Tashkent, 100174
K. S. Mamayusupov
New Uzbekistan University
Uzbekistan
Uzbekistan
Khudoyor S. Mamayusupov
54, Mustaqillik Ave., Tashkent, 100007
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Review
For citations:
Haydarov F.H., Ilyasova R.A., Mamayusupov K.S. Pinned gradient measures of SOS model associated with HA-boundary laws on Cayley trees. Nanosystems: Physics, Chemistry, Mathematics. 2025;16(2):154-163. https://doi.org/10.17586/2220-8054-2025-16-2-154-163
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