Intuitive

The Ising model consists of a linear chain (or lattice) where at each node we have an either an arrow that points upwards or an arrow that points downwards. The force between two neighboring lattice nodes depends on whether they point in the same direction or not.

Concrete

• The best introduction can be found in Critical point phenomena: universal physics at large length scales by Bruce, A.; Wallace, D. published in the book "The New Physics", edited by P. Davies.
• Another great introduction can be found here.
• See also An introduction to the Ising model by Barry A. Cipra, which is a good introduction for beginners.

The Ising model was originally devised as a simplified model of a ferromagnet, but is applicable also in a much broader sense. There is no need to refer to any ferromagnetic setup, but instead the Ising model can be defined completely general.

Recommended Resources

• A Python simulation of the 2D Ising model, can be downloaded here.

Why is it interesting?

The Ising model is the simplest model with a critical point and thus ideal to understand notions like critical exponents and the renormalization group in a simplified setup.

FAQ

Where does the Ising model come from?

Source: Where do quantum field theories come from? by McGreevy

In what forms does the Ising model appear?

Source: Where do quantum field theories come from? by McGreevy

Abstract

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History

• A good summary of the history of the Ising model can be found in History of the lenz-ising model by Stephen G. Brush.
• A more personal account is The Fate of Ernst Ising and the Fate of his Model by Thomas Ising et. al.