In this paper, we consider the two-state Hard-Core model on the closed Cayley tree of branching ratio two. On the symmetric case, we exactly solve the model and show that there is a phase transition.
| Mualliflar | Makhammadaliev M.T., Karshiboev O.Sh. |
|---|---|
| Jurnal | O‘zbekiston matematika jurnali |
| Nashriyot | Ўзбекистон Республикаси ФА Математика институти |
| ISSN | 2010-7269 |
| Nashr sanasi | 2025-09-06 |
| Jild | 69 |
| Son | 3 |
| Betlar | 126-133 |
| Til | Ingliz |
| Ilmiy soha | Fizika-matematika |
| DOI | 10.29229/uzmj.2025-3-13 |
| Indeksga qo‘shilgan | 2026-08-26 |
DOI: 10.29229/uzmj.2025-3-13 · Maqolaning asl sahifasi
closed Cayley tree, Gibbs measure, Hard-Core model, phase transition
| APA | Makhammadaliev M.T., & Karshiboev O.Sh. (2025). The phase transition for the Hard-Core model on the closed Cayley tree of branching ratio two. O‘zbekiston matematika jurnali, 69(3), 126-133. https://doi.org/10.29229/uzmj.2025-3-13 |
|---|---|
| GOST (OAK) | Makhammadaliev M.T., Karshiboev O.Sh. The phase transition for the Hard-Core model on the closed Cayley tree of branching ratio two // O‘zbekiston matematika jurnali. – 2025. – T. 69, № 3. – P. 126-133. – DOI: 10.29229/uzmj.2025-3-13. |
| MLA | Makhammadaliev M.T., and Karshiboev O.Sh. “The phase transition for the Hard-Core model on the closed Cayley tree of branching ratio two.” O‘zbekiston matematika jurnali, 69(3), 126-133, 2025. https://doi.org/10.29229/uzmj.2025-3-13 |
| Chicago | Makhammadaliev M.T., and Karshiboev O.Sh. “The phase transition for the Hard-Core model on the closed Cayley tree of branching ratio two.” O‘zbekiston matematika jurnali, 69(3), 126-133 (2025). https://doi.org/10.29229/uzmj.2025-3-13 |
| Harvard | Makhammadaliev M.T., and Karshiboev O.Sh (2025) ‘The phase transition for the Hard-Core model on the closed Cayley tree of branching ratio two’, O‘zbekiston matematika jurnali, 69(3), 126-133. https://doi.org/10.29229/uzmj.2025-3-13 |
| BibTeX | @article{makhammadalievmt2025,
title = {The phase transition for the Hard-Core model on the closed Cayley tree of branching ratio two},
author = {Makhammadaliev M.T. and Karshiboev O.Sh.},
journal = {O‘zbekiston matematika jurnali},
year = {2025},
volume = {69},
number = {3},
pages = {126-133},
doi = {10.29229/uzmj.2025-3-13},
url = {https://doi.org/10.29229/uzmj.2025-3-13}
} |
Boshqa maqola uchun iqtibos tayyorlash
We study a differential game of two pursuers and one evader, whose dynamics are described by linear differential equations, in $\mathbb{R}^n$. The control functions of pursuers and evader are subjected to the Grönwall…
In approximate integration, an interesting and relevant problem is the construction of formulas with a minimum number of nodes for a given algebraic degree of accuracy.
Let $G~$be finite Jordan domain bounded a Dinismooth curve $\Gamma ~$in the complex plane. Marcinkiewiczmultiplierand Littlewood-Paley type theorems in Smirnov-Orliczclasses, defined in domain $G$, are proved.
The problem of recovering surfaces by the total or extrinsic curvature is related to the solution of the nonlinear elliptic equation of the Monge-Ampere type. Using the geometric method, the existence and uniqueness of…
In this paper, a real analogue of a quasitrace is given, and its connection with the quasitrace of the enveloping C*-algebra is found.Similar to the complex case, some interesting properties of a quasitrace and the…
In this paper, we present exact solution of haploid Markov chain model that describes the fluctuation of gene frequency under the influence of mutation. Also generalizing Markov chain model we introduce and investigate…
In this paper, we address the construction of an optimal quadrature formula in the sense of Sard within a Hilbert space composed of periodic, complex-valued functions, specifically for the purpose of numerically…
This paper discusses the frequent occurrence of the Hadamard type integral equation of the first kind in solving problems in aerodynamics, fluid dynamics, wave propagation theory, and ecology. Since the exact solution…
This paper considers the problem of representing a given natural number as combination of two prime numbers and the square of a third prime number taken from an arithmetic progression. It was the rst to establish the…
This paper proposes a method for solving the problems of the Euler - Bernoulli beam, in which the problem is reduced to the solution of the Fredholm integral equation of the second kind. This integral equation is solved…
O‘zbekiston matematika jurnali — barcha maqolalar · 2025-yil arxivi
This article presents the results of 2018-2023, such as biological diversity, inter-landscape distribution characteristics, density,and number of straggly insects identified from natural and anthropogenic areas of…
This article observational data on the species composition, distribution, population, density, and seasonal damage caused causedby herbivorus bugs. Observationes were carried out in April and September 2021. When…
In the article, the research fields of some species belonging to Paeonia, their significance in human life, adaptation features tovarious ecological conditions are highlighted, and the ecologist groups and other…
This article studies the number of species, population density of terrestrial mollusks of the Topalangdarya basin, located in theSurkhandarya region of Uzbekistan, in various altitudinal regions and biotopes and…
This article sheds light on changes in biomass formation and antimicrobial activity against test pathogenic strains under theinfluence of epigenetic modifiers and elicitors of the endophytic fungus Penicillium…
Shahimardonsoy covered issues such as the soil in the river basin and measures to increase its condition, salinity and fertility, theflora and fauna present in the basin landscape and their conservation.