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

Definitions
The Ising model can often be difficult to evaluate numerically if there are many states in the system. Consider an Ising model with
L = |Λ|: the total number of sites on the lattice, σj ∈ {−1, … See more

• In the ferromagnetic case there is a phase transition. At low temperature, the Peierls argument proves positive magnetization for … 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 = … See more

One of Democritus' arguments in support of atomism was that atoms naturally explain the sharp phase boundaries observed in materials , as when ice melts to water or water turns to … See more

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