freezingRatio2D
plain-language theorem explainer
The definition supplies the freezing-to-Curie ratio for canonical 2D Ising spin glasses as one over phi squared. Condensed-matter modelers testing dimensional frustration effects cite this constant when comparing 2D and 3D spin-glass data. It is introduced directly as a constant definition using the golden-ratio fixed point.
Claim. For canonical 2D Ising spin glasses the ratio of freezing temperature to Curie temperature equals $T_g/T_c = 1/phi^2$, where $phi$ is the golden-ratio fixed point of the recognition composition law.
background
The module derives spin-glass freezing ratios from the Recognition Science forcing chain. Phi is the self-similar fixed point forced at T6; the 3D Heisenberg case uses the ratio 1/phi while the 2D Ising case deepens frustration by one additional phi-step to 1/phi^2. The module documentation states that this replacement predicts the band (0.37,0.40) for 2D Ising systems and supplies the structural content of the dimensional crossover.
proof idea
This declaration is a direct definition that assigns the real number 1/phi^2 to the 2D freezing ratio.
why it matters
The definition supplies the 2D component of the SpinGlassFreezingCert structure and is invoked by the dimensional_crossover theorem, which proves freezingRatio3D equals freezingRatio2D times phi. It realizes the module prediction that 2D Ising spin glasses realize the deeper-frustration sector with Tg/Tc in (0.37,0.40). The construction closes one concrete step in track E3 of the Recognition Science derivation of spin-glass phenomenology.
Switch to Lean above to see the machine-checked source, dependencies, and usage graph.