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.

翻译：摘要：我们基于假设检验提出了一种新的相变表征方法。在该框架中，相变被定义为热力学极限下参数扰动消失时统计不可区分性的破缺。这一视角提供了一个通用且无需序参量的理论框架，不依赖于特定模型或学习过程。研究表明，传统方法（如基于Binder参数的方法）可被重新解释为该框架的特例。作为具体实现，我们采用了一种无需分布假设的双样本游程检验，并证明在不预先知晓序参量的情况下，二维伊辛模型的临界点能被准确识别。