Phase Transitions as the Breakdown of Statistical Indistinguishability

TL;DR

This paper proposes a new hypothesis testing-based framework to characterize phase transitions as the loss of statistical indistinguishability, applicable without model-specific assumptions.

Contribution

It introduces a general, order-parameter-free approach to identify phase transitions, exemplified by accurately detecting the Ising model's critical point using a distribution-free test.

Findings

The framework reinterprets traditional methods like the Binder parameter.

Successfully identifies the Ising model's critical point without prior order parameter knowledge.

Provides a distribution-free method applicable to various models.

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.