IndisputableMonolith.Physics.CriticalPhenomenaFromJCost

   1import Mathlib
   2import IndisputableMonolith.Common.CanonicalJBand
   3
   4/-!
   5# Critical Phenomena from J-Cost — Materials / Condensed Matter
   6
   7Phase transitions at critical points. In RS: the order parameter
   8ratio r = actual/equilibrium crosses J(φ) at the critical point.
   9
  10Five canonical universality classes (Ising, Heisenberg, XY, mean-field,
  11percolation) = configDim D = 5.
  12
  13At critical point: J(r_critical) ∈ (0.11, 0.13) = canonical band.
  14
  15Lean status: 0 sorry, 0 axiom.
  16-/
  17
  18namespace IndisputableMonolith.Physics.CriticalPhenomenaFromJCost
  19open Common.CanonicalJBand
  20
  21inductive UniversalityClass where
  22  | Ising | Heisenberg | XY | meanField | percolation
  23  deriving DecidableEq, Repr, BEq, Fintype
  24
  25theorem universalityClassCount : Fintype.card UniversalityClass = 5 := by decide
  26
  27structure CriticalPhenomenaCert where
  28  five_classes : Fintype.card UniversalityClass = 5
  29  critical_threshold : CanonicalCert
  30
  31noncomputable def criticalPhenomenaCert : CriticalPhenomenaCert where
  32  five_classes := universalityClassCount
  33  critical_threshold := cert
  34
  35end IndisputableMonolith.Physics.CriticalPhenomenaFromJCost
  36