IndisputableMonolith.CondensedMatter.SpinGlassFreezingRatio
The module states the freezing-to-Curie ratio for canonical 3D Heisenberg spin glasses as 1/φ. Condensed matter researchers cite it when mapping Recognition Science constants onto spin glass transition data. The module assembles a set of definitions and supporting statements for the 3D case together with 2D and crossover variants.
claimThe freezing-to-Curie ratio for canonical 3D Heisenberg spin glasses equals $1/φ$, where $φ$ is the self-similar fixed point of the Recognition Composition Law.
background
The module belongs to the CondensedMatter domain and imports the RS time quantum τ₀ = 1 tick from IndisputableMonolith.Constants. It introduces the freezing ratio together with positivity and band constraints for both three- and two-dimensional spin glasses, using the phi-ladder and J-cost structure supplied by the upstream forcing chain. The local setting places spin glass freezing inside the eight-tick octave and the D = 3 spatial structure forced at T8.
proof idea
This is a definition module, no proofs.
why it matters in Recognition Science
The module supplies the explicit ratio that downstream declarations such as SpinGlassFreezingCert and spin_glass_one_statement apply to certify spin glass behavior. It closes the step from the T5 J-uniqueness and T6 phi fixed point to an observable condensed-matter quantity.
scope and limits
- Does not derive the ratio from microscopic Hamiltonians.
- Does not treat quantum corrections or itinerant electrons.
- Does not cover time-dependent aging or memory effects.
- Applies the primary statement only to canonical 3D Heisenberg glasses.