Origin of the classical magnetization discontinuities of the dodecahedron

TL;DR

This paper explains the origin of the three magnetization discontinuities in the classical Heisenberg model on a dodecahedron, linking them to geometric frustration and magnetic response characteristics, with implications across different interaction limits.

Contribution

It identifies the specific origins of the magnetization jumps in the dodecahedron model, connecting them to the Ising limit and frustration effects, and analyzes their behavior across interaction regimes.

Findings

Highest-field discontinuity linked to saturation at the Ising limit.

Discontinuities persist up to the XY limit, then vanish.

Lower-field jumps result from competition of plateau-related discontinuities.

Abstract

The classical antiferromagnetic Heisenberg model on the dodecahedron has been shown to have three magnetization discontinuities in an external field. Here it is shown that the highest-field discontinuity can be directly traced back to the strong magnetization jump leading to saturation at the Ising limit, which originates from the magnetic response of an isolated pentagon and the frustrated connectivity of the dodecahedron. This discontinuity survives up to the $XY$ limit and disappears shortly before the ferromagnetic Ising interaction fully polarizes the spins. The two lower-field jumps of the model result from the competition of discontinuities that emerge from the magnetization plateau surviving away from the Ising limit.