We propose a structural diagnostic for thermal phase transitions based on the product of two correlation-derived quantities: the nearest-neighbor mutual information Iₙn and the magnetic susceptibility χ. Key Result The thermal cliff diagnostic: κT = Ĩₙn × χ̃ exhibits a sharp peak (cliff) near the critical temperature in systems possessing genuine phase transitions. Findings System Result 2D Ising Sharp cliff near Tc ≈ 2. 269 1D Ising No cliff (null test confirmed) Finite-size scaling Tₚeak (L) → Tc as L → ∞ Contents paper/ — Full manuscript (LaTeX and Markdown) figures/ — Publication-quality figures (PDF and PNG) data/ — Numerical results (CSV format) code/ — Python simulation scripts (Numba-accelerated Monte Carlo) Reproducibility pip install numpy numba matplotlib python code/thermalcliffₛcaling. py
Takayuki Takagi (Sun,) studied this question.