On the Equivalence of Trapped Colloids, Pinned Vortices, and Spin Ice

Abstract

We investigate the recently reported analogies between pinned vortices in nano-structured superconductors or colloids in optical traps, and spin ice materials. The frustration of the two models, one describing colloids and vortices, the other describing spin ice, differs essentially. However, their effective energetics is made identical by the contribution of an emergent field associated to a topological charge. This equivalence extends to the local low-energy dynamics of the ice manifold, yet breaks down in lattices of mixed coordination, because of topological charge transfer between sub-latices.