The Ising model (or Lenz–Ising model), named after the physicists Ernst Ising and Wilhelm Lenz, is a mathematical model of ferromagnetism See more

Definitions
The Ising model can often be difficult to evaluate numerically if there are many states in the system. … See more

• In the ferromagnetic case there is a phase transition. At low temperature, the Peierls argument proves positive magnetization for the nearest neighbor case and then, by the Griffiths inequality, also when longer range interactions are added. Meanwhile, … See more

Consider a set $${\displaystyle \Lambda }$$ of lattice sites, each with a set of adjacent sites (e.g. a graph) forming a $${\displaystyle d}$$-dimensional … See more

The most studied case of the Ising model is the translation-invariant ferromagnetic zero-field model on a d-dimensional lattice, namely, Λ = Z , Jij = 1, h = 0.
No phase transition … See more

One of Democritus' arguments in support of atomism was that atoms naturally explain the sharp phase boundaries observed in materials … See more

The thermodynamic limit exists as long as the interaction decay is $${\displaystyle J_{ij}\sim |i-j|^{-\alpha }}$$ with α > 1.
• In the case of ferromagnetic interaction See more