rushbrooke_relation_2D
plain-language theorem explainer
The Rushbrooke scaling relation holds for the exact 2D Ising exponents with α = 0, β = 1/8 and γ = 7/4. Statistical mechanicians cite the identity when verifying consistency of critical exponents in solvable models. The proof substitutes the three constant definitions and reduces the resulting arithmetic equality.
Claim. $α + 2β + γ = 2$ where α = 0, β = 1/8, γ = 7/4 are the 2D Ising critical exponents (logarithmic divergence treated as α = 0).
background
The module derives universal critical exponents from φ-scaling near phase transitions. Quantities diverge as C ~ |t|^{-α}, M ~ (-t)^β, χ ~ |t|^{-γ} with t the reduced temperature. Universality follows because J-cost fluctuations inherit φ-structure, constraining the exponents independently of microscopic details.
proof idea
The term proof unfolds the three sibling definitions (alpha_2D_Ising := 0, beta_2D_Ising := 1/8, gamma_2D_Ising := 7/4) then applies norm_num to the arithmetic identity.
why it matters
The declaration supplies a consistency check inside the φ-scaling derivation of critical exponents. It confirms the Rushbrooke relation for the exactly solvable 2D Ising case before the module proceeds to 3D values. The parent module targets the paper proposition that golden-ratio scaling enforces all scaling relations.
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