近日，法国巴黎萨克雷大学David Clément团队报道了跨相变序参量的非高斯统计量。相关论文发表在2026年7月22日出版的《自然》杂志上。

二级相变以临界标度行为和普适性为特征。特别地，相变过程中热力学量的奇异行为由该相变所属普适类的临界指数决定。然而，临界性质也可以通过序参量在整个相变过程中的概率分布来表征，其中预期存在非高斯统计特征，但这方面在很大程度上仍缺乏研究。

研究组利用动量空间中的单原子分辨探测技术，测量了相互作用晶格玻色气体在连续相变过程中序参量振幅的完整概率分布。结果发现，这些涨落可由一个有效势——通过类比朗道理论从测得的概率分布中重构得到——来描述；该有效势在超流（有序）相中呈现一个非平凡极小值，并在相变点处消失。

此外，研究组在相变点附近观察到序参量的非高斯统计特征，表现为非零的高阶累积量发生突变性的符号反转。研究组通过数值计算表明，这些累积量的符号反转在均匀系统中满足临界标度行为，并且其实验表现无法由经典模型复现，但可以被低温量子模型所捕捉。该结果突显了序参量统计在探测临界现象和普适性方面的关键作用。

附：英文原文

Title: Non-Gaussian statistics of the order parameter across a phase transition

Author: Allemand, Maxime, Dupuy, Graud, Paquiez, Paul, Dupuis, Nicolas, Ranon, Adam, Roscilde, Tommaso, Chalopin, Thomas, Clment, David

Issue&Volume: 2026-07-22

Abstract: Second-order phase transitions are characterized by critical scaling and universality1. The singular behaviour of thermodynamic quantities at the transition, in particular, is determined by critical exponents of the universality class of the transition. However, critical properties are also characterized by the probability distribution of the order parameter across the transition2,3, in which non-Gaussian statistics are expected4,5,6, but remain largely unexplored7. Here, making use of single-atom-resolved detection in momentum space8, we measure the full probability distribution of the order-parameter amplitude across a continuous phase transition in an interacting lattice Bose gas9. We find that fluctuations are captured by an effective potential—reconstructed from the measured probability distribution by analogy with Landau theory10—displaying a non-trivial minimum in the superfluid (ordered) phase, which vanishes at the transition point. Moreover, we observe non-Gaussian statistics of the order parameter near the transition, distinguished by non-zero high-order cumulants undergoing abrupt sign changes. We show numerically that these sign changes of the cumulants obey critical scaling in homogeneous systems, and that their experimental behaviour is not reproduced by classical models, whereas it is captured by a low-temperature quantum model. Our results underscore the crucial role of order parameter statistics in probing critical phenomena and universality.

DOI: 10.1038/s41586-026-10811-1

Source: https://www.nature.com/articles/s41586-026-10811-1