The Ising model

The Ising Model. Spin up/down is shown as white/black.

Perhaps the most beautiful and elegant model of all times. Atoms of spin up and down are arranged on a 2D-lattice, interacting only with their nearest neighbours. At low temperatures all spins are aligned. At high temperatures, spins are randomly distributed. At a certain critical temperature, a phase transition occurs, which captures all the essential features of a real magnetic system. The model has been studied and build upon for almost a century and keeps fascinate and surprise scientists world-wide. There is plenty to be done and much to be learned!

Suitable for: First year project, Bachelor’s project

Main disciplines: Programming (any language), complex systems, phase transitions

Related work:

The Ising Model on Wikipedia