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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.

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

\vec{s}_i \in \mathbb{R}^3, |\vec{s}_i|=1,

each one placed on a lattice node.

The model is defined through the following Hamiltonian:

\mathcal{H} = -\sum_{i,j} \mathcal{J}_{ij} \vec{s}_i \cdot \vec{s}_j


\mathcal{J}_{ij} = \begin{cases} J & \mbox{if }i, j\mbox{ are neighbors} \\ 0 & \mbox{else.}\end{cases}

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

This article is licensed under the GNU Free Documentation License. It uses material from the Wikipedia article "Heisenberg_model_(classical)". A list of authors is available in Wikipedia.
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