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

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.