Mean field models for spin glasses

Translation from physics: ‘Glass’: a material which is hard and inflexible (like a solid) but is not completely ordered or lattice-like in its microscropic structure (thus, unlike a crystal or simple metals). ‘Spin’: pertaining to the magnetic spins of ions in a material. ‘Spin glass’: a material, effectively solid, which contains some irregular distribution of magnetizable ions. Basic laboratory examples: Cadmium telluride (a non-magnetizable crystalline compound of cadmium and tellurium) doped some easily-magnetized atoms, e.g. of iron or nickel. Some weak natural examples: meteorites1. Spin glasses are complicated because the magnetic interactions between ions depend heavily on the exact distance between them, the irregular distances in a spin glass give rise to irregular interactions and hence a locally highly-complicated response to an external magnetic field. (Possible application: verification that a rock is a meteorite1.) I learned this from a stranger on a bus who hunts meteorites for a living, so I won’t swear by it.