Researchers from the Hong Kong University of Science and Technology, together with colleagues from the University of Tokyo, have proposed a general theory that clearly distinguishes when two states of matter remain distinct phases and when they smoothly transform into one another. The work resolves a long-standing dispute about the behavior of water ice at extremely high pressure and at the same time provides a universal tool for describing magnetic systems with different spin values.
The key to understanding lies in symmetry. Liquid water and steam, for example, possess the same symmetry: their molecules have no preferred direction. Therefore, beyond the critical point they transform into one another without a sharp boundary and are considered a single phase. Ice, however, forms a crystal lattice, breaking this symmetry, and is therefore always separated from the liquid by a true phase boundary.
In the case of the dense forms of ice — VII, VIII and X — the oxygen atoms form one and the same framework structure, and the differences concern only the arrangement of the hydrogen atoms. In ice VII the hydrogens occupy random positions, in VIII they are ordered, and in X they sit exactly midway between the oxygens. The average symmetry of the crystal is the same for VII and X, and for a long time it remained unclear whether they are separate phases or different manifestations of one.
The scientists reformulated the problem in the language of magnetism. The midpoints of the bonds between oxygen atoms form a pyrochlore lattice — the very one on which the famous "spin ices" are built. The three possible positions of the hydrogen correspond to three states of the magnetic moment with spin 1. In a simplified model that disregards the ordering of VIII, ices VII and X are separated by a sharp transition only at absolute zero. At any finite temperature, thermal defects behave like magnetic monopoles, screen the field and turn the sharp boundary into a smooth crossover. Thus, VII and X belong to one phase, while VIII remains separate because of its broken symmetry.
The main paper in Physical Review X generalizes the result to arbitrary spin values in classical pyrochlore spin-ice models. It turned out that the phases are separated by a network of defect strings: as long as the strings are closed, the states are distinct. On heating, the monopoles break the strings, and the distinction disappears. An exception is spin 3/2, where a sharp transition between two liquid-like magnetic states persists at finite temperature and ends in a critical point without an external field — a promising target for future experiments.
Professor Haruki Watanabe emphasized: the results confirm that the phases of ordinary matter are classified exclusively by broken symmetry. Wherever symmetry does not distinguish states, there exists a continuous path without a phase boundary. Researchers are now searching for topological phases that could exist at finite temperature beyond this classification.
The new theory not only closes an old ice puzzle but also opens the way to predicting the behavior of complex magnetic materials, nanomagnetic arrays and cold-atom systems.
