gamma_2D_Ising
plain-language theorem explainer
gamma_2D_Ising supplies the exact value 7/4 for the magnetic susceptibility critical exponent in the two-dimensional Ising model. Physicists studying phase transitions and scaling relations cite this definition when checking consistency with Rushbrooke, Widom, and Fisher relations. The definition is a direct assignment drawn from the φ-scaling universality in Recognition Science.
Claim. In the two-dimensional Ising model the susceptibility exponent satisfies $γ = 7/4$.
background
The module derives universal critical exponents from RS φ-scaling near phase transitions. Critical phenomena are described by power-law divergences: specific heat $C ∼ |t|^{-α}$, order parameter $M ∼ (-t)^β$, susceptibility $χ ∼ |t|^{-γ}$, and correlation length $ξ ∼ |t|^{-ν}$, with reduced temperature $t = (T - T_c)/T_c$. Universality holds because exponents depend only on dimensionality and symmetry, and in Recognition Science they arise from φ-structured fluctuations in J-cost.
proof idea
The declaration is a direct definition that assigns the constant 7/4 to gamma_2D_Ising.
why it matters
This definition supplies the numerical input required by the scaling relation theorems fisher_relation_2D, rushbrooke_relation_2D, and widom_relation_2D in the same module. It realizes the target of deriving universal critical exponents from φ-scaling as stated in the module documentation, linking to the Recognition Science mechanism where J-cost fluctuations enforce φ-constrained exponents. The result aligns with the exact solution for the 2D Ising model and supports the paper proposition on golden ratio scaling.
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