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.
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 fieldNeighboring 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:
The Ising Model in Python by Mr. P Solver
. Source. The dude is crushing it on a Jupyter Notebook. New to topics? Read the docs here!