Phase Transitions as the Breakdown of Statistical Indistinguishability
This work provides a general, order-parameter-free framework for detecting phase transitions, which could be useful for complex systems where conventional order parameters are unknown.
The authors propose a new definition of phase transitions based on hypothesis testing, where a phase transition is marked by the breakdown of statistical indistinguishability under small parameter changes. They validate their framework by accurately identifying the critical point of the 2D Ising model without prior knowledge of the order parameter.
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.