Irrational moments and signatures of higher-rank gauge theories in diluted classical spin liquids

Classical spin liquids (CSLs) have proved to be a fruitful setting for the emergence of exotic gauge theories. Vacancy clusters in CSLs can introduce gauge charges into the system, and the resulting behavior in turn reveals the nature of the underlying theory. We study these effects for a series of CSLs on the honeycomb lattice. We find that dilution leads to the emergence of effective free spins with tuneable, and generally irrational, size. For a specific higher-rank CSL, described by a symmetric tensor gauge fields, dilution produces non-decaying spin textures with a characteristic quadrupolar angular structure, and infinite-ranged interactions between dilution clusters.