Heisenberg 3D Modell

ETH-Zürich 2024

Github: https://github.com/daniel-schwarzenbach/Heisenberg-3D-model/

Read the: Documentation

In a Nutshell

The Heisenberg model describes a system of quantum spins with nearest-neighbor interactions. The spins are arranged on a three-dimensional lattice.

Physical Relevance:

• Used to model magnetic properties of real materials.
• Serves as a prototype for studying quantum phase transitions and critical phenomena.
• In 3D, the Heisenberg model can exhibit magnetic long-range order at low temperatures (spontaneous magnetization).

The Hameltonian \(Ĥ\) dertermines the energy of the lattice for a given spin configuration \(σ\): \[Ĥ(\vec{σ}) = - J \sum_{\langle i,j ⟩} \sigma_i σ_j - h \sum \sigma_i\]

where the Spins are an normalised Vector in 3D space: \[σ_i ∈ [0,2π)×(-\frac{\pi}{2}, \frac{\pi}{2})∪ \{+z,-z\} \quad ∀ i\]

\(h\): external magnetic field.

\(J\): interaction strength.