N-vector model

The n-vector model or O(n) model is one of the many highly simplified models in the branch of physics known as statistical mechanics. In the n-vector model, n-component, unit length, classical spins $\mathbf{s}_i$ are placed on the vertices of a lattice. The Hamiltonian of the n-vector model is given by:

$H = -J{\sum}_{<i,j>}\mathbf{s}_i \cdot \mathbf{s}_j$