Insights gained from solvable models into a variety of phase transitions, including emergent assemblies plus isoelectronic series of atomic ions
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 rareearth metals, and secondly, via the 3d Ising model, to critical behavior 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 modeling on real materials.
 Publication:

International Journal of Modern Physics B
 Pub Date:
 November 2014
 DOI:
 10.1142/S0217979214300199
 arXiv:
 arXiv:1411.0219
 Bibcode:
 2014IJMPB..2830019M
 Keywords:

 Phase transitions;
 melting;
 Curie and Néel temperatures;
 de Gennes factor;
 Isoelectronic atomic ions;
 75.10.Hk;
 75.50.Ee;
 31.15.p;
 Classical spin models;
 Antiferromagnetics;
 Calculations and mathematical techniques in atomic and molecular physics;
 Condensed Matter  Statistical Mechanics;
 Condensed Matter  Strongly Correlated Electrons;
 Physics  Atomic and Molecular Clusters
 EPrint:
 to appear in Int. J. Mod. Phys. B