Researchers at Nanyang Technological University in Singapore and Chinese institutions report that tipping points in physical systems can exhibit a smooth doughnut-like topological structure, challenging the traditional separation between critical phenomena and topology.

A doughnut (torus) serves as the topological analogy to illustrate a hole in the structure, contrasting with a sphere that has no hole, highlighting qualitative differences in their properties.

The work suggests topology and critical phenomena, long treated as distinct, may be connected at thresholds where systems rapidly change states.

The researchers sought to determine whether doughnut-like topological properties can exist at critical points, where physical systems undergo dramatic transitions in behaviour.

The study, published in Nature on October 7, features co-first authors Cheng Zheyu and Zhang Xiuhai affiliated with NTU, signaling collaboration across Singapore and China.