Ising model (1920)

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: stanford.edu/~jeffjar/statmech/intro4.html 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 neighbor interaction? What likes to be with what? And aren't different phases in different crystal structures?

Also has some funky relations to renormalization TODO.

Bibliography:

stanford.edu/~jeffjar/statmech/intro4.html

Video 24.

The Ising Model in Python by Mr. P Solver

. Source. The dude is crushing it on a Jupyter Notebook.

Table of contents 216 4

 Ancestors (8)

 Incoming links (1)

Renormalization