What question did this study set out to answer?

The aim is to explore the hidden structure of phase transitions in the 3D Ising model using advanced statistical methods.

July 10, 2026Open Access

Double-Peak Splitting: The Hidden Structure of Finite-Lattice Phase Transitions in the 3D Ising Model

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Randomized trial reveals deep phase transition structures in the 3D Ising model, implying new detection methods.

The aim is to explore the hidden structure of phase transitions in the 3D Ising model using advanced statistical methods.
Implemented the Bai-Perron double-break blind test on a 64x64 lattice.
Applied the Multi-Regime State Decoupling Algorithm on 3D Ising and 2D Potts q=4 models.
Used cross-validation and bootstrap regression methods for robustness verification.
Detected double-peak splitting of second-order phase transitions with a statistical confidence of p = 3.33×10⁻⁷⁰.
Confirmed stable regime switch temperature across multiple lattice sizes, independent of the thermodynamic limit.
Achieved a robust verification closure on an NP-complete system while redefining finite-size effects.

Tang (2026) studied this question.

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