Heisenberg model (classical)

The Heisenberg model is the n = 3 case of the n-vector model, one of the models used in statistical physics to model ferromagnetism, and other phenomena.

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It can be formulated as follows: take a d-dimensional lattice, and a set of spins of the unit length

,

each one placed on a lattice node.

The model is defined through the following Hamiltonian:

with

a coupling between spins.

The general mathematical formalism used to describe and solve the Heisenberg model and certain generalizations is developed in the article on the Potts model.

See also

• Heisenberg model (quantum)
• Ising model
• XY model