Phase Transitions as the Breakdown of Statistical Indistinguishability

2026-04-21 · Source: cs.AI updates on arXiv.org · Field: Science & Research — Physical Sciences & Chemistry, Mathematics & Computational Sciences · Depth: Expert, long

Summary

Taiyo Narita and Hideyuki Miyahara introduce a novel framework for characterizing phase transitions, defining them as the breakdown of statistical indistinguishability under vanishing parameter perturbations in the thermodynamic limit. This approach offers a general, order-parameter-free, and model-independent method, contrasting with traditional techniques that rely on specific order parameters or data-driven machine learning. The authors demonstrate that conventional methods, such as those utilizing the Binder parameter, can be reinterpreted as special cases within their hypothesis testing framework. As a concrete application, they employ a distribution-free two-sample run test to accurately identify the critical point of the two-dimensional Ising model without prior knowledge of its order parameter. Numerical simulations show a sharp dip in the test statistic at the critical temperature, with deviations reaching 4-5 standard deviations, confirming the rejection of the null hypothesis of statistical indistinguishability.

Key takeaway

For research scientists working on many-body systems, this framework offers a robust, order-parameter-free method for detecting phase transitions. You should consider implementing this statistical distinguishability approach, especially when traditional order parameters are unknown or difficult to define, as it provides a quantitative criterion for identifying critical points with controlled significance levels and reduced statistical error compared to moment-ratio-based methods.

Key insights

Phase transitions can be defined as the breakdown of statistical indistinguishability under vanishing parameter perturbations.

Principles

• Phase transitions are order-parameter-free.
• Conventional methods are special cases of hypothesis testing.

Method

A two-sample run test compares probability distributions from nearby parameters, reducing their separation as system size increases to detect statistical distinguishability breakdown.

In practice

• Apply distribution-free two-sample tests.
• Use $\Delta T(N) = \Delta T_0 (N/N_0)^{-x}$ for parameter separation.

Topics

• Phase Transitions
• Statistical Indistinguishability
• Hypothesis Testing
• Two-Sample Run Test
• Ising Model

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Editorial summary, takeaway, and curation by AIssential. Original article published by cs.AI updates on arXiv.org.