The forging of strong correlations on decreasing temperature can take place without the arousal of conventional order. If this happens, as in some geometrically frustrated magnets, disorder can be a phenomenon more interesting than order itself. A Coulomb phase, for example, has critical-like pair-spin correlations, leading to neutron scattering pinch points and emergent electromagnetism; its local excitations are quasiparticles behaving as magnetic monopoles.

In this talk we present a new instance of disorder in an Ising pyrochlore lattice: the Polarized Monopole Liquid (PML), a dense monopole fluid with pinch points in the magnetic charge-pair correlations. It is a phase of ``monopole matter" never considered before, which can be stabilized in real materials using a magnetic field and uniaxial stress along the [100] direction. To explain how the monopole correlations arise, we show that the PML is a Coulomb phase in which spin fluctuations cannot be assigned either to monopoles or to internal magnetic moments, but necessarily comprehend both degrees of freedom. We will use a simple but nontrivial method to Helmholtz decompose the spin field into a divergenceless and a divergenceful part in magnetic charge disordered pyrochlores that shows the appearance of pinch points associated to the divergenceful component in places where Bragg peaks are observed for the ``all-in/all-out" antiferromagnet.