# Discontinuous classical ground state magnetic response as an even-odd effect in higher order rotationally invariant exchange interactions

## TL;DR

This paper reveals that higher order rotationally invariant exchange interactions in the classical Heisenberg model cause discontinuous magnetic responses, with even-odd effects depending on the order of interactions, highlighting the importance of microscopic interaction details.

## Contribution

It demonstrates that adding higher order exchange interactions induces discontinuities in the ground state magnetization, revealing even-odd effects related to the order of interactions.

## Key findings

- Discontinuous ground state responses occur with higher order exchange interactions.
- The number of discontinuities depends on the parity of the interaction order q.
- Results hold for both bipartite and frustrated triangular lattices.

## Abstract

The classical ground state magnetic response of the Heisenberg model when rotationally invariant exchange interactions of integer order q>1 are added is found to be discontinuous, even though the interactions lack magnetic anisotropy. This holds even in the case of bipartite lattices which are not frustrated, as well as for the frustrated triangular lattice. The total number of discontinuities is associated with even-odd effects as it depends on the parity of q via the relative strength of the bilinear and higher order exchange interactions, and increases with q. These results demonstrate that the precise form of the microscopic interactions is important for the ground state magnetization response.