A chain of tiny magnets that should stay disordered at any ordinary temperature may behave differently when enclosed with light between mirrors. Researchers at Yokohama National University have shown, in an exactly solvable mathematical model, how a cavity can help a one-dimensional spin chain develop magnetic order and a shared light field.
The result addresses a long-standing limit of a simple model of magnetism. In 1925, physicist Ernst Ising showed that a single one-dimensional chain, where each magnetic particle interacts only with its nearest neighbors, cannot undergo a magnetic phase transition at finite temperatures. A phase transition is a change in the overall state of a system, such as particles shifting from disordered to organized. In higher dimensions, magnetic transitions can happen, and the Ising model has become a key way to study how groups of particles behave.
The Yokohama team asked whether trapped light could change the one-dimensional chain’s usual behavior. They studied a chain of classical Ising spins coupled to one mode of light inside a mirror-box cavity. In such a setup, light and matter interact strongly. The model shows that cavity photons can connect the spins over long distances, rather than letting each spin affect only its immediate neighbors.
That added connection makes the difference. The researchers found that the coupled system undergoes a second-order magnetic phase transition at a particular temperature. The spins develop long-range magnetic order, while a large, coherent light field builds up in the cavity. The chain on its own would not make this change at finite temperature; the light-mediated interaction allows it.
The team also derived the magnetization, the number of photons and the critical temperature—the point at which the transition occurs—exactly. Because the model can be solved precisely, it gives scientists a clear reference for understanding more complicated systems where light and matter interact. Earlier work on one-dimensional cavity systems had focused on their behavior at absolute zero. This study instead examines the transition at finite temperatures, closer to the conditions relevant for thermal equilibrium.
“We wanted to understand how interactions inside matter affect a superradiant phase transition at thermal equilibrium,” said Motoaki Bamba, an associate professor in Yokohama National University’s Faculty of Engineering. Superradiance here means the spontaneous buildup of a coherent electromagnetic field as light and matter interact. Bamba said many simple models leave out interactions that are present in real materials.
The work, by Shuntaro Otake and colleagues, was published in Physical Review Research in 2026 as “Exactly solvable phase transition in a cavity-coupled one-dimensional Ising chain.” The researchers now want to include energy loss and study more realistic systems. They point to superconducting-qubit arrays and one-dimensional magnets coupled to sub-terahertz cavities as possible experimental platforms. The exact model does not establish that the effect has already been observed in those devices, but it offers a way to guide future tests—and to explore how light might help control the phases of materials.