# Continuous ground-state degeneracy of classical dipoles on regular lattices

## TL;DR

This paper explains how finite point-symmetry in classical dipolar systems leads to unexpected continuous ground-state degeneracy, providing new insights into their theoretical understanding.

## Contribution

It reveals the mechanism by which finite point-symmetry causes continuous degeneracy in classical dipolar systems, advancing the theoretical framework.

## Key findings

- Finite point-symmetry induces continuous ground-state degeneracy.
- Provides a theoretical explanation for degeneracy in dipolar systems.
- Enhances understanding of complex dipolar-coupled magnetic systems.

## Abstract

Dipolar interactions are crucial in the modeling of many complex magnetic systems, such as the pyrochlores and artificial spin systems. Remarkably, many classical dipolar coupled spin systems exhibit a continuous ground-state degeneracy, which is unexpected as the Hamiltonian does not possess a continuous symmetry. In this paper, we explain, how such a finite point-symmetry leads to a continuous ground-state degeneracy of specific classical dipolar-coupled systems. This work, therefore, provides new insight into the theory of classical dipolar-coupled spin-systems and opens the way to understand more complex dipolar coupled systems.