The multiple symmetry sustaining phase transitions of spin ice

We present the full phase diagram of the dumbbell model of spin ice as a function of temperature, chemical potential and staggered chemical potential which breaks the translational lattice symmetry in favour of charge crystal ordering. We observe a double winged structure with five possible phases, monopole fluid (spin ice), fragmented single monopole crystal phases and double monopole crystal, the zinc blend structure. Our model provides a skeleton for liquid-liquid phase transitions and for the winged structures observed for itinerant magnets under pressure and external field. We relate our results to recent experiments on Ho$_2$Ir$_2$O$_7$ and propose a wide ranging set of new experiments that exploit the phase diagram, including high pressure protocols, dynamical scaling of Kibble-Zurek form and universal violations of the fluctuation-dissipation theorem.