SIMULATION MODELS

An Ising model portrait of Ernst Ising

Using a 100 year old model of magnetism to create a “meta” image of its namesake

Well, have you? (source: J. van Saders)

What is the Ising model?

Lenz’s insight into modeling magnets and Ising’s thesis

In 1920, German physicist Wilhelm Lenz was looking for a simplified model to explain why magnets “demagnetize” when heated sufficiently. He envisioned an array of magnetic dipoles with “spins” point up or down (represented by arrows):

A 2D array of magnetic dipoles with spins up or down used to model a ferromagnetic material in the Ising model. (source: J. van Saders)

Conceptually, if most of the spins pointed the same way then the fusing of the aligned dipole fields would create a magnet. As the spins randomized (through heating), the fields would tend to cancel and neutralize large scale magnetism.

Lenz assigned his graduate student Ernst Ising to work out the mathematics, which became his thesis (Ising 1925). Ising further simplified the model to a one dimensional string of dipoles where two nearest neighbors would influence a dipole’s spin. His analysis showed that even at low temperatures, all the spins didn’t align. Both Ising and Lenz assumed the result…