The n-vector model or O(n) model has been 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 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 and denotes the standard Euclidean inner product. Special cases of the n-vector model are:
- || The Self-Avoiding Walks (SAW)
- || 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.
- H. E. Stanley, "Dependence of Critical Properties upon Dimensionality of Spins," Phys. Rev. Lett. 20, 589-592 (1968).
 H. E. Stanley, "Dependence of Critical Properties upon Dimensionality of Spins," Phys. Rev. Lett. 20, 589-592 (1968).
This paper is the basis of many articles in field theory and is reproduced as Chapter 1 of Brèzin/Wadia [eds] The Large-N expansion in Quantum Field Theory and Statistical Physics (World Scientific, Singapore, 1993). Also described extensively in the text Pathria RK Statistical Mechanics: Second Edition (Pergamon Press, Oxford, 1996).
- P.G. de Gennes, Phys. Lett. A, 38, 339 (1972) noticed that the case corresponds to the SAW.
- George Gaspari, Joseph Rudnick, Phys. Rev. B, 33, 3295 (1986) discuss the model in the limit of going to 0.
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