中国物理学家发现临界点具有环面拓扑结构，挑战物理学传统观念
Chinese discovery of doughnut-like topology at tipping points breaks physics convention
中国物理学家发现，物理系统发生状态突变的临界点可具有类似甜甜圈孔洞的光滑数学结构，挑战临界现象与拓扑必须分开研究的传统观念。研究由新加坡和中国机构人员完成，南洋理工大学的 Cheng Zheyu 与 Zhang Xiuhai 为共同第一作者，成果发表于 Nature。
Chinese physicists have discovered that a tipping point – a threshold where a physical system rapidly shifts states – can possess a smooth mathematical structure resembling a doughnut’s hole, challenging a belief that the two phenomena must be studied separately.
For decades, mainstream physicists have mostly treated critical phenomena, which describe how physical systems change at critical points, and topology, which studies the properties of geometry, as separate areas of research.
A classic illustration of topology is the difference between a sphere and a doughnut. The two cannot be transformed into each other by stretching or bending alone because they have a different number of holes, unless the surface is cut or glued.
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The study by researchers at Singaporean and Chinese institutions was published in Nature on October 7, with Cheng Zheyu and Zhang Xiuhai, both affiliated with Nanyang Technological University in Singapore, as co-first authors.
Cheng and his colleagues set out to investigate whether doughnut-like topological properties could exist at critical points – the thresholds at which physical systems change their behaviour.
来源：南华早报 · scmp.com