This article has been reviewed according to Science X's editorial process and policies. Editors have highlighted the following attributes while ensuring the content's credibility: A research team led by Haruki Watanabe, a professor in the Department of Physics and the Jockey Club Institute for Advanced Study (IAS) at The Hong Kong University of Science and Technology (HKUST), in collaboration with professor Yukitoshi Motome and graduate student Sena Watanabe from the University of Tokyo, has developed a unified theory that predicts when two states of matter are genuinely distinct and when they are actually the same. The work provides a general framework for classifying phases across magnetic systems with different spin values and resolves a long-standing debate surrounding the behavior of water ice under extreme pressure.
The paper, titled "Topological phase transitions and their thermodynamic fate in arbitrary-𝑆 classical pyrochlore spin ice," is published in Physical Review X. Whether phases of matter are separated by a sharp boundary often depends on symmetry. For example, while liquid water and steam are commonly regarded as different states, they actually share the same underlying symmetries—meaning their molecules have no preferred position or direction.
As a result, they can be continuously transformed into one another beyond a specific critical point, making them a single thermodynamic phase. Ice, by contrast, forms a crystal lattice in which molecules occupy fixed positions, breaking a symmetry preserved by liquids and gases. Because these symmetries differ, ice must remain separated from liquid by a genuine phase boundary.
The researchers applied this principle to high-pressure forms of ice, including ice VII, ice VIII and ice X. These forms share the same framework of oxygen atoms but differ in the arrangement of their hydrogen atoms. In ice VII, hydrogen atoms occupy random positions, while in ice VIII they adopt an ordered arrangement, and in ice X they are located midway between neighboring oxygen atoms.
Despite these differences, ice VII and ice X preserve the same underlying crystal symmetries when averaged over time, creating long-standing uncertainty over whether they represent distinct phases of matter or different manifestations of the same phase. To address this question, the team recast the problem in terms of magnetism. The midpoints of the bonds between oxygen atoms form a pyrochlore lattice, the structure behind "spin ice" magnets, and the three positions available to each hydrogen atom correspond exactly to the three states of a magnetic moment of spin 1.
A related study led by the team, published in Physical Review B, showed that, in a simplified model excluding ice VIII ordering, ice VII and ice X are separated by a sharp transition only at absolute zero. At any temperature above absolute zero, thermally excited defects act like magnetic monopoles and screen the field that holds the two states apart, dissolving the sharp transition into a gradual crossover. As a result, ice VII and ice X belong to the same phase.
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