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.

Additional recommended knowledge

Guide to balance cleaning: 8 simple steps

How to quickly check pipettes?

Daily Sensitivity Test

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

Guide to balance cleaning: 8 simple steps

How to quickly check pipettes?

Daily Sensitivity Test

See also

About chemeurope.com

About LUMITOS

Advertise with LUMITOS