![]() “This universality result is even more intriguing” because it means that the same patterns emerge regardless of the differences between models of physical systems, said Hugo Duminil-Copin of the Institute of Advanced Scientific Studies (IHES) and the University of Geneva.ĭuminil-Copin is a co-author of the work along with Karol Kajetan Kozlowski of the École Normale Supérieure in Lyon, Dmitry Krachun of the University of Geneva, Ioan Manolescu of the University of Fribourg and Mendes Oulamara of IHES and Paris-Saclay University. The new proof breaks from this history and marks the first time that rotational invariance has been proved to be a universal phenomenon across a broad class of models. In the context of physical systems on the brink of phase changes, it means many properties of the system behave the same regardless of how a model of the system is rotated.Įarlier results had established that rotational invariance holds for two specific models, but their methods were not flexible enough to be used for other models. Rotational invariance is a symmetry exhibited by the circle: Rotate it any number of degrees and it looks the same. This was open for a long time,” said Gady Kozma of the Weizmann Institute of Science in Israel. The work establishes that rotational invariance - one of the three symmetries contained within conformal invariance - is present at the boundary between states in a wide range of physical systems. Now, in a proof posted in December, a team of five mathematicians has come closer than ever before to proving that conformal invariance is a necessary feature of these physical systems as they transition between phases. ![]() The powerful symmetry, known as conformal invariance, is actually a package of three separate symmetries that are all wrapped up within it. For more than 50 years, mathematicians have been searching for a rigorous way to prove that an unusually strong symmetry is universal across physical systems at the mysterious juncture where they’re changing from one state into another.
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