Correlation Ceilings and Thermal Cliffs: A Structural Diagnostic of Phase Transitions

We propose a structural diagnostic for thermal phase transitions based on the product of two correlation-derived quantities: the nearest-neighbor mutual information I_nn and the magnetic susceptibility χ. Key Result The thermal cliff diagnostic: κ_T = Ĩ_nn × χ̃ exhibits a sharp peak (cliff) near the critical temperature in systems possessing genuine phase transitions. Findings System Result 2D Ising Sharp cliff near T_c ≈ 2.269 1D Ising No cliff (null test confirmed) Finite-size scaling T_peak(L) → T_c 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/thermal_cliff_scaling.py