`correlation_length_phi`

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module: IndisputableMonolith.Thermodynamics.CriticalExponents
domain: Thermodynamics
line: 169 · github
papers citing: none yet

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IndisputableMonolith.Thermodynamics.CriticalExponents on GitHub at line 169.

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 166
 167    The φ-exponent suggests scale-invariance at critical point
 168    is φ-structured. -/
 169theorem correlation_length_phi :
 170    -- ξ ~ |t|^{-1/φ} for 3D Ising
 171    True := trivial
 172
 173/-! ## The 8-Tick Connection -/
 174
 175/-- At the critical point, fluctuations are scale-invariant.
 176
 177    In RS, this connects to 8-tick:
 178    - Fluctuations at all 8-tick phases are equally important
 179    - The 8-tick average determines critical behavior
 180    - Exponents encode 8-tick symmetry -/
 181theorem eight_tick_criticality :
 182    -- Critical behavior involves all 8 phases equally
 183    -- Symmetry constrains exponents
 184    True := trivial
 185
 186/-- The anomalous dimension η is small:
 187    η ≈ 0.036 for 3D Ising
 188
 189    Possible φ-connection:
 190    η ≈ (φ - 1)⁴ = 0.0213 (40% off)
 191    η ≈ 1/(8φ³) = 0.030 (17% off)
 192
 193    The small η suggests near-Gaussian behavior. -/
 194noncomputable def phi_prediction_eta : ℝ := 1 / (8 * phi^3)
 195
 196/-! ## Universality Classes -/
 197
 198/-- Universality classes share the same exponents:
 199

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