🤖 AI Summary
This work proposes a universal framework for identifying phase transitions without requiring order parameters or prior knowledge of the underlying model. Building on the hypothesis that infinitesimal parameter perturbations break statistical indistinguishability in the thermodynamic limit, the study redefines phase transitions as abrupt changes in distributional distinguishability. This perspective enables a model-agnostic, training-free detection method implemented via a distribution-free two-sample runs test. The approach unifies conventional criteria—including the Binder cumulant—and accurately locates the critical point in the two-dimensional Ising model, thereby demonstrating both its validity and broad applicability across different systems.
📝 Abstract
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.