Clustering of Topological Charges in a Kagome Classical Spin Liquid

Fractionalization is a ubiquitous phenomenon in topological states of matter. In this work, we study the collective behavior of fractionalized topological charges and their instabilities, through the $J_1$-$J_2$-$J_3$ Ising model on a kagome lattice, which can be mapped to a model of interacting topological charges under the constraint of Gauss' law. We find that the recombination of topological charges gives rise to a yet unexplored classical spin liquid. This spin liquid is characterized by an extensive residual entropy, as well as the formation of hexamers of same-sign topological charges. The emergence of hexamers is reflected to a half-moon signal in the magnetic structure factor, which provides us a signature of this new spin liquid in neutron-scattering experiments. To study this phase, a worm algorithm has been developed which does not require the usual divergence-free condition.