A Simple Highly Accurate Algebraic Model of Phase Transitions on Square, Hexagonal, and Triangular Flat Faces

E. V. Votyakov; Вотяков Е. В.; Yu. K. Tovbin; Товбин Ю. К.

doi:10.31857/S0044453723060298

A Simple Highly Accurate Algebraic Model of Phase Transitions on Square, Hexagonal, and Triangular Flat Faces

Authors: Votyakov E.V.¹, Tovbin Y.K.²
Affiliations:
1. Cyprus Institute, Energy Environment and Water Research Center
2. Kurnakov Institute of General and Inorganic Chemistry, Russian Academy of Sciences
Issue: Vol 97, No 6 (2023)
Pages: 763-772
Section: ПРОБЛЕМЫ, ТЕНДЕНЦИИ РАЗВИТИЯ И АКТУАЛЬНЫЕ ЗАДАЧИ ФИЗИЧЕСКОЙ ХИМИИ
Submitted: 27.02.2025
Published: 01.06.2023
URL: https://ruspoj.com/0044-4537/article/view/668712
DOI: https://doi.org/10.31857/S0044453723060298
EDN: https://elibrary.ru/KDDUZX
ID: 668712

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Abstract

A simple, highly accurate algebraic model is proposed for describing phase transitions on flat faces of square, hexagonal, and triangular structures. The model is derived using the cluster variational approach within the Ising model and expressed in an analytical form by choosing a basic closed-form cluster of the minimal size for each facet structure with nearest neighbors of z = 3 (triangular), 4 (square), and 6 (hexagonal). The new model provides three times more accurate equations for molecular distributions of particles in the Ising model than earlier analytical expressions. The model’s analytical equations allow direct calculations of molecular distributions. (Only iterative numerical means were used earlier to obtain results of the same accuracy.) The effect of refinements when considering correlation effects in the new model is compared to traditional mean-field and quasi-chemical (QCA) approximations when calculating isotherms and pair and cluster distribution functions. Analytical expressions are obtained for the critical temperature of a segregation-type phase transition.

Keywords

correlation effects, Ising model, cluster variational approach, critical temperature, phase transitions molecular distributions

About the authors

E. V. Votyakov

Cyprus Institute, Energy Environment and Water Research Center

Email: karaul@gmail.com
2121, Nicosia, Cyprus

Yu. K. Tovbin

Kurnakov Institute of General and Inorganic Chemistry, Russian Academy of Sciences

Author for correspondence.
Email: karaul@gmail.com
119991, Moscow, Russia

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