# The multiple symmetry sustaining phase transitions of spin ice

## TL;DR

This paper maps the full phase diagram of spin ice's dumbbell model, revealing complex phase transitions and structures, and connects these findings to experimental observations and potential future experiments.

## Contribution

It provides a comprehensive phase diagram of the dumbbell model of spin ice, including new phases and structures, and links theoretical results to experimental systems and protocols.

## Key findings

- Identified a double winged phase structure with five phases.
- Connected phase transitions to experimental systems like Ho$_2$Ir$_2$O$_7$.
- Proposed new experimental protocols based on the phase diagram.

## Abstract

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.