Phase Transitions in Chemistry
Synchronism correctly predicts WHERE phase transitions occur (at the γ ≈ 1 boundary) but fails to predict HOW they unfold (critical exponents are 2× off).
What the Coherence Function Gets Right
Melting/Boiling
Phase transitions happen at the γ ≈ 1 boundary where coherence changes rapidly. The function correctly identifies which materials have higher/lower transition temperatures relative to each other.
Superconductivity
Cooper pairs represent 2-body correlations (Ncorr = 2, γ = √2). The transition to superconductivity is a coherence phase transition.
Superfluidity
Bose-Einstein condensation = macroscopic quantum coherence. The entire fluid has Ncorr = N (all particles correlated), driving γ → 0.
Magnetic Transitions
Curie/Néel temperatures mark coherence transitions in spin systems. Correctly located but spin-orbit coupling dominates, which C(ρ) ignores.
What It Gets Wrong
Critical Exponents: 2× Off
Real phase transitions belong to universality classes with specific critical exponents (β, γ, δ, etc.). The tanh form gives mean-field exponents, which differ from observed values by ~2×. This is a known limitation of any mean-field theory — fluctuations near the critical point matter, and C(ρ) doesn't account for them.
Mean-Field LimitationMelting Points: 53% Average Error
Crystal structure, defects, impurities, and multi-body effects dominate actual melting behavior. A single coherence parameter cannot capture this complexity.
53% Error