Correction to: Nature Reviews Physics https://doi.org/10.1038/s42254-019-0118-3, published online 8 November 2019.

In the version of this article originally published, ref. 42 was listed (Möller & Moessner, Phys. Rev. Lett. https://doi.org/10.1103/PhysRevLett.96.237202 (2006)) but a second reference by the same authors was mistakenly omitted and is now included as ref. 94 (Möller, G. & Moessner, R. Magnetic multipole analysis of kagome and artificial spin-ice dipolar arrays. Phys. Rev. B. 80, 140409 (2009)) in the HTML and PDF versions of the article.