N-vector model

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In statistical mechanics, the n-vector model or O(n) model is a simple system of interacting spins on a crystalline lattice. It was developed by H. Eugene Stanley as a generalization of the Ising model, XY model and Heisenberg model.[1] In the n-vector model, n-component unit-length classical spins are placed on the vertices of a d-dimensional lattice. The Hamiltonian of the n-vector model is given by:

where the sum runs over all pairs of neighboring spins and denotes the standard Euclidean inner product. Special cases of the n-vector model are:

: The self-avoiding walk[2][3]
: The Ising model
: The XY model
: The Heisenberg model
: Toy model for the Higgs sector of the Standard Model

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