beta_3D_Ising
plain-language theorem explainer
The declaration assigns the numerical value 0.3265 to the order-parameter exponent β for the three-dimensional Ising universality class. A condensed-matter physicist would cite it when comparing Recognition Science φ-scaling predictions to magnetization data near critical points. The definition is a direct numerical assignment with no further computation or derivation steps.
Claim. In the three-dimensional Ising model the order-parameter exponent satisfies β = 0.3265, so that the magnetization scales as M ∼ (−t)^β with reduced temperature t = (T − T_c)/T_c.
background
Critical phenomena near phase transitions exhibit power-law divergences characterized by universal exponents: specific heat C ∼ |t|^{-α}, order parameter M ∼ (−t)^β, susceptibility χ ∼ |t|^{-γ}, and correlation length ξ ∼ |t|^{-ν}. Recognition Science traces this universality to φ-structured fluctuations in J-cost, which depend only on dimensionality and symmetry class rather than microscopic details. The module THERMO-005 targets derivation of these exponents from RS φ-scaling, with the 3D Ising class providing the benchmark values α ≈ 0.11, β ≈ 0.326, γ ≈ 1.24, ν ≈ 0.63.
proof idea
Direct numerical assignment of the accepted literature value for the 3D Ising order-parameter exponent.
why it matters
This definition supplies one of the critical exponents required for the Recognition Science derivation of universal scaling near phase transitions. It populates the set needed for the paper proposition on Universal Critical Exponents from Golden Ratio Scaling. The assigned value is consistent with T8 forcing of D = 3 and the eight-tick octave structure in the UnifiedForcingChain.
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