Monopole ordered phases in dipolar and nearest-neighbors Ising pyrochlore: From spin ice to the all-in–all-out antiferromagnet

We study Ising pyrochlores by means of Monte Carlo simulations. We cover a set of exchange constants ranging from the frustrated ferromagnetic case (spin-ice) to the fully-ordered ``all-in--all-out'' antiferromagnet in the dipolar model, reinterpreting the results---as in an ionic system---in terms of a temperature vs magnetic charge density phase diagram. In spite of its spin nature and the presence of both double and single nonconserved magnetic charges, the dipolar model gives place to a phase diagram which is quite comparable with those previously obtained for on-lattice systems of electric charges, and on spin ice models with a conserved number of single magnetic charges. The contrast between these systems, to which we add results from the nearest-neighbors model, put forward other features of our phase diagram---notably, a monopole fluid with charge order at high monopole densities that persists up to arbitrarily high temperatures---that can only be explained taking into account construction constraints forced by the underlying spin degrees of freedom.