pith. sign in
def

delta_3D_Ising

definition
show as:
module
IndisputableMonolith.Thermodynamics.CriticalExponents
domain
Thermodynamics
line
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plain-language theorem explainer

The declaration supplies the numerical value 4.789 for the critical isotherm exponent δ in the three-dimensional Ising universality class. Physicists modeling magnetic phase transitions under Recognition Science φ-scaling would reference this constant when fitting magnetization curves at criticality. It is introduced as a direct real-number assignment without further derivation in the module.

Claim. The critical isotherm exponent δ for the three-dimensional Ising model is defined by δ = 4.789.

background

The module THERMO-005 targets derivation of universal critical exponents from RS φ-scaling. Near a phase transition, quantities diverge as powers of reduced temperature t = (T - T_c)/T_c: specific heat ~ |t|^{-α}, order parameter ~ (-t)^β, susceptibility ~ |t|^{-γ}, correlation length ~ |t|^{-ν}. Universality follows from φ-structured J-cost fluctuations, independent of microscopic details but dependent on dimensionality and symmetry. The upstream result from ClassicalBridge.Fluids.CPM2D.model builds a Model from a Hypothesis bundle by setting C, defectMass, orthoMass, energyGap and tests.

proof idea

The definition is a direct constant assignment of the approximate numerical value 4.789. No lemmas or tactics are applied; it is a noncomputable real constant chosen to match known 3D Ising behavior.

why it matters

This definition contributes the δ value to the set of critical exponents supporting universal scaling from φ in the Recognition Science framework, as stated in the module target for the paper 'Universal Critical Exponents from Golden Ratio Scaling'. It completes the 3D Ising list alongside sibling definitions for α, β, γ, ν and η. No downstream uses are recorded, leaving open integration with exact φ-ladder or RCL derivations.

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