Translation-invariant p-adic quasi Gibbs measures for the Potts model with an external field on the Cayley tree
https://doi.org/10.17586/2220-8054-2025-16-2-164-175
Abstract
The study is focused on investigation of p-adic Gibbs measures for the q-state Potts model with an external field and determination of the conditions for the existence of a phase transition. In this work, we derive a functional equation that satisfies the compatibility condition for p-adic quasi-Gibbs measures on a Cayley tree of order k ≥ 2. Furthermore, we prove that if |q|p = 1 there exists a unique p-adic Gibbs measure for this model. Additionally, for the Potts model on a binary tree, we identify three p-adic quasi-Gibbs measures under specific circumstances: one bounded and two unbounded, which implies a phase transition.
Keywords
p-adic numbers,
the Potts model with external field,
p-adic quasi Gibbs measure,
translationinvariant,
Cayley tree
Supporting agencies: The authors thank Akbarkhuja M. Tukhtabaev for valuable advice and an anonymous referee for helpful suggestions that improved the paper.
About the Authors
M. M. Rakhmatullaev
V. I. Romanovskiy Institute of Mathematics, Uzbekistan Academy of Sciences; New Uzbekistan University
Uzbekistan
Uzbekistan
Muzaffar M. Rakhmatullaev
University str. 9, 100174,Tashkent
100000, Tashkent, Uzbekistan
N. D. Samijonova
Namangan State University
Uzbekistan
Uzbekistan
Nurkhon D. Samijonova –
161, Boburshox str, 160107, Namangan
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For citations:
Rakhmatullaev M.M., Samijonova N.D. Translation-invariant p-adic quasi Gibbs measures for the Potts model with an external field on the Cayley tree. Nanosystems: Physics, Chemistry, Mathematics. 2025;16(2):164-175. https://doi.org/10.17586/2220-8054-2025-16-2-164-175
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