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:

:

where the sum runs over all pairs of neighboring spins 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.