The wiki comments:
The Bohr–van Leeuwen theorem, discovered in the 1910s, showed that classical physics theories are unable to account for any form of magnetism, including ferromagnetism. Magnetism is now regarded as a purely quantum mechanical effect. Ferromagnetism arises due to two effects from quantum mechanics: spin and the Pauli exclusion principle.
Toy model of matter that exhibits phase transition in dimension 2 and greater. It does not provide numerically exact results by itself, but can serve as a tool to theorize existing and new phase transitions.
Each point in the lattice has two possible states: TODO insert image.
As mentioned at: some systems which can be seen as modelled by it include:
  • the spins direction (up or down) of atoms in a magnet, which can undergo phase transitions depending on temperature as that characterized by the Curie temperature and an externally applied magnetic field
    Neighboring spins like to align, which lowers the total system energy.
  • the type of atom at a lattice point in a 2-metal alloy, e.g. Fe-C (e.g. steel). TODO: intuition for the neighbour interaction? What likes to be with what? And aren't different phases in different crystal structures?
Also has some funky relations to renormalization TODO.
TODO what it means to solve an Ising model in general? gives some good notions:
  • is the expectation value of the value. It is therefore a number between -1.0 an and 1.0, -1.0 means everything is always down, 0.0 means half up half down, and 1.0 means all up
  • : correlation between neighboring states. TODO.
A tiny idealized magnet! It is a very good model if you have a small strong magnet interacting with objects that are far away, notably other magnetic dipoles or a constant magnetic field.
The cool thing about this model is that we have simple explicit formulas for the magnetic field it produces, and for how this little magnet is affected by a magnetic field or by another magnetic dipole.
This is the perfect model for electron spin, but it can also be representative of macroscopic systems in the right circumstances.
The intuition for the name is likely that "dipole" means "both poles are on the same spot".
Figure 1. Different macroscopic magnets can be approximated by a magnetic dipole when shrunk seen from far away. Source.
Applications: produce high magnetic fields for
As of the early 2020s, superconducting magnets predominantly use low temperature superconductors Nb-Ti and Nb-Sn, see also most important superconductor materials, but there were efforts underway to create practical high-temperature superconductor-based magnets as well: Section "High temperature superconductor superconducting magnet".
Wikipedia has done well for once:
The current to the coil windings is provided by a high current, very low voltage DC power supply, since in steady state the only voltage across the magnet is due to the resistance of the feeder wires. Any change to the current through the magnet must be done very slowly, first because electrically the magnet is a large inductor and an abrupt current change will result in a large voltage spike across the windings, and more importantly because fast changes in current can cause eddy currents and mechanical stresses in the windings that can precipitate a quench (see below). So the power supply is usually microprocessor-controlled, programmed to accomplish current changes gradually, in gentle ramps. It usually takes several minutes to energize or de-energize a laboratory-sized magnet.
They are pioneers in making superconducting magnets, physicist from the university taking obsolte equipment from the uni to his garage and making a startup kind of situation. This was particularly notable for this time and place.
They became a major supplier for Magnetic resonance imaging applications.