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# 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:

$H = -J{\sum}_{}\mathbf{s}_i \cdot \mathbf{s}_j$

where the sum runs over all pairs of neighboring spins < i,j > and $\cdot$ denotes the standard Euclidean inner product. Special cases of the n-vector model are: