pith. sign in
def

eta_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 0.0364 for the anomalous dimension in the three-dimensional Ising universality class. Researchers in statistical mechanics cite this constant when matching Recognition Science φ-scaling predictions to lattice data or experiments on 3D Ising systems. The definition is a direct numerical assignment of the accepted value, placed inside the module's φ-scaling treatment of critical exponents.

Claim. The anomalous dimension for the three-dimensional Ising model is given by $η = 0.0364$.

background

Near a critical point the correlation function decays as $r^{-(d-2+η)}$ at $T=T_c$, where η is the anomalous dimension. The module THERMO-005 treats all critical exponents as consequences of φ-scaling: J-cost fluctuations near criticality are constrained by the golden-ratio fixed point, yielding universal numbers that depend only on dimension and symmetry class. For the 3D Ising class (Z_2 symmetry in three spatial dimensions) the module lists the accepted numerical values, including this one for η.

proof idea

The definition is a direct numerical assignment of the accepted value 0.0364. No lemmas or tactics are applied; the constant is introduced as a module-level definition for later use in exponent relations.

why it matters

This definition populates the set of 3D Ising exponents required by the paper proposition 'Universal Critical Exponents from Golden Ratio Scaling'. It supplies the concrete number that the φ-scaling mechanism (T5 J-uniqueness and the self-similar fixed point) must reproduce for D=3. The precise derivation from the forcing chain remains open in the current module.

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