## The symmetry of phase transitions

Different physical systems exhibit the same characteristics when they transition from one state to another. This finding by five mathematicians could help clarify whether an even deeper conjecture about a fundamental behavior of matter is correct.

The fact that materials sometimes suddenly change their properties when exposed to external influences such as temperature changes fascinated mankind even in ancient times. The physical descriptions of such phase transitions reveal exciting symmetries, which is why mathematicians are now also dealing with the area. In December 2020, a research team published an astonishing result: A wide variety of systems turn out to be rotationally invariant if they continuously transition from one phase to another - regardless of their microscopic details.

The prime example of a rotationally symmetrical figure is a circle. No matter which side you look at it from, it always looks identical. Applied to physical systems, this means that their observable properties do not change when they are rotated. While it was previously known that some models are rotationally invariant near phase transitions, the question remained unanswered for many others.

The authors of the new work were able to demonstrate rotational symmetry for a broad class of systems for the first time. It is therefore not an isolated case, but a universal phenomenon …

Article "Mathematicians Prove Symmetry of Phase Transitions" translated and edited by "Spektrum der Wissenschaft" from "Quanta Magazine", an independent magazine of the Simons Foundation devoted to the dissemination of research in mathematics and the natural sciences has set as a goal.