String-like defects decide when two spin-ice phases stay distinct, a new theory argues

Symmetry alone could not sort ice VII from ice X. Averaged over time, the two keep the same crystal symmetries, and that left the question open for years ^[3]. The symmetry test does work elsewhere. Liquid water and steam share their symmetries and can be transformed into one another continuously beyond the critical point, while ice breaks a symmetry the liquid keeps, so a genuine boundary must separate them ^[12].

The team mapped the ice structure onto a pyrochlore spin model. The midpoints of the bonds between oxygen atoms form a pyrochlore lattice, and the three positions open to each hydrogen atom match the three states of a spin-1 magnetic moment ^[4]. In that picture, heat matters because it creates defects that behave like magnetic monopoles, and the monopoles cut the strings open ^[10]. Once a string is cut, the distinction it protected washes out ^[10].

For water, the work leans on an earlier Physical Review B study by the same group ^[5]. That study used a model without ice VIII ordering. In it, ice VII and ice X are separated by a sharp transition only at absolute zero, and ice VIII stays distinct because its ordered hydrogen arrangement breaks a crystal symmetry ^[5][6].

The Physical Review X paper, by Haruki Watanabe of HKUST with Yukitoshi Motome and Sena Watanabe of the University of Tokyo, generalizes that to classical pyrochlore spin-ice models with arbitrary spin ^[1][2][7]. Phys.org's account says the work resolves a long-standing debate about water ice under extreme pressure ^[14]. In our view that claim should be read narrowly. The ice conclusion comes from the simplified model, and the new paper's own subject is spin-ice models. The paper does not test whether real ice under pressure follows a model that excludes the ordering of ice VIII.

One inference follows from the spin values. Ice maps onto spin 1, a whole number ^[4], and the only exception to the crossover rule is spin 3/2 ^[11]. The ice mapping therefore sits on the crossover side of the divide ^[13]. Spin 3/2 is where the authors predict something different: an abrupt transition between two distinct liquid-like magnetic states that survives at finite temperature and ends at a critical point with no external field ^[11]. Phys.org's account calls it an especially promising target for future experiments ^[11].