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

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

each one placed on a lattice node.

The model is defined through the following Hamiltonian:

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

with

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

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.

Heisenberg model (classical)

Additional recommended knowledge

Better weighing performance in 6 easy steps

Recognize and detect the effects of electrostatic charges on your balance

Daily Visual Balance Check

See also

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