Thermodynamic Comparison and the Ideal Glass Transition of A Monatomic Systems Modeled as an Antiferromagnetic Ising Model on Husimi and Cubic Recursive Lattices of the Same Coordination Number

TL;DR

This study compares thermodynamic properties and glass transition behaviors of a monatomic system modeled by an antiferromagnetic Ising model on two recursive lattices with the same coordination number but different structures, revealing their similarities and differences.

Contribution

It introduces exact solutions of an antiferromagnetic Ising model on two recursive lattices to analyze thermodynamics and glass transitions in monatomic systems.

Findings

Both lattices exhibit similar transition temperatures and thermodynamic behaviors.

Interactions beyond nearest neighbors significantly influence the system's properties.

Different unit cell structures still produce comparable thermodynamic results.

Abstract

Two kinds of recursive lattices with the same coordination number but different unit cells (2-D square and 3-D cube) are constructed and the antiferromagnetic Ising model is solved exactly on them to study the stable and metastable states. The Ising model with multi-particle interactions is designed to represent a monatomic system or an alloy. Two solutions of the model exhibit the crystallization of liquid, and the ideal glass transition of supercooled liquid respectively. Based on the solutions, the thermodynamics on both lattices was examined. In particular, the free energy, energy, and entropy of the ideal glass, supercooled liquid, crystal, and liquid state of the model on each lattice were calculated and compared with each other. Interactions between particles farther away than the nearest neighbor distance are taken into consideration. The two lattices show comparable properties on the transition temperatures and the thermodynamic behaviors, which proves that both of them are practical to describe the regular 3-D case, while the different effects of the unit types are still obvious.