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 are placed on the vertices of a lattice. The Hamiltonian of the n-vector model is given by:

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where the sum runs over all pairs of neighboring spins < i,j > and 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.