Ising Model

The Ising model is a mathematical model of ferromagnetism in statistical mechanics, consisting of discrete variables called spins, each of which can take one of two values, arranged on a lattice so that each spin interacts only with its nearest neighbors. The model is named after the physicist Ernst Ising, who solved the one dimensional version in his 1924 doctoral thesis, working under Wilhelm Lenz, who had proposed the model; the two dimensional square lattice version was famously solved exactly by Lars Onsager in 1944 and shows a genuine phase transition at a critical temperature, unlike the one dimensional case. Despite its simplicity, the Ising model captures the essential mechanism by which local interactions between many small units can produce large scale collective behavior, and beyond its original use in physics it has since been applied to neural networks, biological systems and social behavior wherever many interacting units can be modeled as taking one of two states.