beta_2D_Ising
plain-language theorem explainer
The declaration supplies the exact value of the order-parameter critical exponent β for the two-dimensional Ising model. Researchers working on critical phenomena in low dimensions cite this constant when verifying scaling relations such as Rushbrooke and Widom identities. It is introduced as a direct numerical assignment drawn from the known exact solution of the 2D Ising model.
Claim. In the two-dimensional Ising model the magnetization exponent satisfies $β = 1/8$.
background
The module derives universal critical exponents from RS φ-scaling near phase transitions. Quantities diverge as C ~ |t|^{-α}, M ~ (-t)^β, χ ~ |t|^{-γ}, and ξ ~ |t|^{-ν}, with t the reduced temperature. The 2D Ising case is exactly solvable, yielding the listed exponents including β = 1/8; these values are constrained by φ-structured fluctuations in J-cost.
proof idea
Direct definition that assigns the known exact solvable value 1/8.
why it matters
This definition supplies the β input required by the Rushbrooke relation (α + 2β + γ = 2) and the Widom relation (γ = β(δ - 1)) for the 2D Ising class. It forms part of the exact-exponent set used to illustrate φ-scaling universality in the paper 'Universal Critical Exponents from Golden Ratio Scaling'. The 2D Ising case serves as a benchmark before extension to three dimensions.
Switch to Lean above to see the machine-checked source, dependencies, and usage graph.