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

Safe Weighing Range Ensures Accurate Results

Daily Visual Balance Check

What is the Correct Way to Check Repeatability in Balances?

See also

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