Insights gained from solvable models into a variety of phase transitions, including emergent assemblies plus isoelectronic series of atomic ions

TL;DR

This paper reviews three exactly solvable models that illuminate various phase transitions, including melting, magnetic transitions, and atomic ionization, by connecting theoretical models with experimental and numerical data.

Contribution

It introduces and analyzes three solvable models for different phase transitions, linking theoretical insights with experimental and numerical results.

Findings

Insights into melting and magnetic phase transitions in heavy rare-earth metals.

Understanding of critical behavior in insulating ferromagnets via the 3d Ising model.

Analysis of atomic ionization in isoelectronic series with decreasing atomic number.

Abstract

Three solvable models are set out in some detail in reviewing different types of phase transitions. Two of these relate directly to emergent critical phenomena, viz. melting and magnetic transitions in heavy rare-earth metals, and secondly, via the $3d$ Ising model, to critical behaviour in an insulating ferromagnet such as CrBr$_3$. The final `transition', however, concerns ionization of an electron in an isoelectronic series with $N$ electrons as the atomic number $Z$ is reduced below that of the neutral atom. These solvable models are, throughout, brought into contact either with experiment, or with very precise numerical modelling on real materials.