Hamiltonian Dynamics of Classical Spins
Abstract
We discuss the geometry behind the classical Heisenberg model at the level suitable for third- or fourth-year students who did not have the opportunity to take a course on differential geometry. The arguments presented here rely solely on elementary algebraic concepts such as vectors, dual vectors and tensors, as well as Hamiltonian equations and Poisson brackets in their simplest form. We derive Poisson brackets for classical spins, along with the corresponding equations of motion for the classical Heisenberg model, starting from the two-sphere geometry, thereby demonstrating the relevance of standard canonical procedures in the case of the Heisenberg model.
Fields of Study & Subjects
Molecular spectroscopy and chirality
Publication details
- Journal / source
- Physics
- Volume
- 8
- Issue
- 1
- Pages
- 23–23
- Publication date
- 25 February 2026
- Language
- EN