pith. sign in
def

freezingRatio2D

definition
show as:
module
IndisputableMonolith.CondensedMatter.SpinGlassFreezingRatio
domain
CondensedMatter
line
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papers citing
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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.

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