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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}_{<i,j>}\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:

n = 0 || The Self-Avoiding Walks (SAW)
n = 1 || The Ising model
n = 2 || The XY model
n = 3 || The Heisenberg model

The general mathematical formalism used to describe and solve the n-vector model and certain generalizations is developed in the article on the Potts model.

This article is licensed under the GNU Free Documentation License. It uses material from the Wikipedia article "N-vector_model". A list of authors is available in Wikipedia.
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