用假设检验定义相变，无需先验知识即可精准定位临界点
Phase Transitions as the Breakdown of Statistical Indistinguishability
- 基于统计不可区分性破裂定义相变，不依赖序参量或模型细节
- 在二维伊辛模型中，无需已知序参量即可准确识别临界点
- 方法适用于传统手段（如Binder系数）的统一重构，具有普适性
我们提出一种基于假设检验的相变新表征方法。在该框架中，相变被定义为热力学极限下微小参数扰动导致的统计不可区分性失效。这一视角提供了一个无序参量、通用且不依赖特定模型洞察或学习过程的统一框架。我们证明，传统方法如基于Binder参数的分析可作为此框架下的特例。具体实现中，采用无分布假设的两样本游程检验，成功在不依赖序参量先验知识的情况下，精确识别出二维伊辛模型的临界点。
原文摘要 · Abstract (English)
We introduce a novel characterization of phase transitions based on hypothesis testing. In our formulation, a phase transition is defined as the breakdown of statistical indistinguishability under vanishing parameter perturbations in the thermodynamic limit. This perspective provides a general, order-parameter-free framework that does not rely on model-specific insights or learning procedures. We show that conventional approaches, such as those based on the Binder parameter, can be reinterpreted as special cases within this framework. As a concrete realization, we employ a distribution-free two-sample run test and demonstrate that the critical point of the two-dimensional Ising model is accurately identified without prior knowledge of the order parameter.
Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品；中文卡片由大模型生成，请以原文为准。