N-vector model

The n-vector model or O(n) model, introduced by H. Eugene Stanley, 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 ${\displaystyle \mathbf {s} _{i}}$ are placed on the vertices of a lattice. The Hamiltonian of the n-vector model is given by:

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

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