The Coulomb phase, with its dipolar correlations and pinch-point-scattering patterns, is central to discussions of geometrically frustrated systems, from water ice to binary and mixed-valence alloys, as well as numerous examples of frustrated magnets
. The emergent Coulomb phase of lattice-based systems has been associated with divergence-free fields and the absence of long-range order. Here, we go beyond this paradigm, demonstrating that a Coulomb phase can emerge naturally as a persistent fluctuating background in an otherwise ordered system. To explain this behavior, we introduce the concept of the fragmentation of the field of magnetic moments into two parts, one giving rise to a magnetic monopole crystal, the other a magnetic fluid with all the characteristics of an emergent Coulomb phase. Our theory is backed up by numerical simulations, and we discuss its importance with regard to the interpretation of a number of experimental results.
We consider an alternative to the usual spin glass paradigm for disordered magnetism, consisting of the previously unstudied combination of frustrated magnetic interactions and pseudo-dipolar disorder in spin positions. We argue that this model repre
sents a general limiting case for real systems as well as a realistic model for certain binary fluorides and oxides. Furthermore, it is of great relevance to the highly topical subjects of the Coulomb phase and `charge ice. We derive an analytical solution for the ground state phase diagram of a model system constructed in this paradigm and identify magnetic phases that remain either disordered or partially ordered even at zero temperature. These phases are of a hitherto unobserved type, but may be broadly classified as either `spin liquids or `semi-spin liquids in contrast to the usual spin glass or semi-spin glass. Numerical simulations are used to show that the spin liquid phase exhibits no spin glass transition at finite temperature, despite the combination of frustration and disorder. By mapping onto a model of uncoupled loops of Ising spins, we show that the magnetic structure factor of this phase acts, in the limit $Trightarrow0$, as a sensitive probe of the positional disorder correlations. We suggest that this result can be generalized to more complex systems, including experimental realizations of canonical spin glass models.
