  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.
