This is an example of a 2D Ising model of ferromagnetism which is a project undertaken in PHY236: Computational Physics. This project is used to study the  temperature dependence of phase transitions in ferromagetic materials.

Here a grid containing 128x128 points represent atomic magnetic field directions as pointing up/down indicated by black/white. The sum of these individual fields can produce some overall magnetic field.  As the system evolves from some initial random state, neighbouring points influence each other via quantum mechanical exchange interactions. This interaction can induce alignment of 

neighbouring magnetic field directions and hence islands of magnetism emerge and develop across the material. In this low temperature example, the local interactions eventually create a fully aligned system.

Values of Mag and MCS specify the normalised magnetic field (0-1) and Monte Carlo 'time' steps respectively. The simulation was written in Python using Numpy and Numba.