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. In the image in the right-hand side a black square means arrow up whereas a white square means arrow down. 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.

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

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

Abstract

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.