arXiv:2604.15773v1 Announce Type: cross
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.

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