One of the most famous models in physics is the Ising model, invented by Wilhelm Lenz as a PhD problem to his student Ernst Ising. The one-dimensional version of it was solved in Ising's thesis in 1924; later, in 1944, Lars Onsager solved the two-dimensional case in the absense of external magnetic field and in a square lattice.
Although primarily a physical model, it is quite fair to say that the model became part of the mathematics literature, since its descriptions and formulations involve many interesting tools from graph theory, combinatorics, measure theory, convex analysis and so on.
Physically, the Ising model can me thought as a system of many little magnets in which case the spins $\pm 1$ represent a magnetic moment. It can also represent a lattice gas, where the spins now represent whether a site is occupied by a particle or not.
I've heard before that the Ising model has a vast number of applications, some of them really interesting and curious. But after coming across the paper Social applications of two-dimensional Ising models, in which the authors use the Ising model to study socio-economic opinions, urban segregation and language change, I got really curious on what else can be done using it. So, the title says it all: what are other interesting and/or surprising applications of the Ising model?
Best Answer
An application of the Ising model in social sciences is to voter models: The dynamics of the Ising model tries to align neighbouring spins, similarly, perhaps, to humans deciding on their political, religious, or consumer preferences [1].
An application to genetics is described in [2], where it is shown that the Ising model with only nearest-neighbor interactions between genetic markers can detect susceptibility loci for type-1 diabetes not previously found by other methods of analysis.
In computer science, the Ising model describes the complexity class of a topological quantum computer based on Majorana fermions [3].
In physics "Ising superconductivity" describes the pairing of electrons in two-dimensional superconducting layered compounds [4].
Phase transition and power-law coarsening in Ising-doped voter model, Adam Lipowski, Dorota Lipowska, Antonio L. Ferreira.
The Ising model in physics and statistical genetics, J. Majewski, H. Li, J. Ott.
A short introduction to topological quantum computation, Ville T. Lahtinen and Jiannis K. Pachos.
Recent progresses in two-dimensional Ising superconductivity, W. Li et al.