# N-vector model

## From Wikipedia, the free encyclopedia

In statistical mechanics, the ** n-vector model** or

**O(**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*) model*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.