OAI/Probability/InvariantIsing/Spectral/SpectralTemperatureFunctional.lean

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7 declarations, 0 contain sorry, 0 declared as axioms

The finite-spectrum temperature functional is a differentiable primitive of the interaction energy, including at temperature zero.

  1. theorem OAI.InvariantIsing.continuous_finiteInteractionEnergy_temperature line 16
  2. def OAI.InvariantIsing.finiteTemperatureFunctional line 40

    Source documentation

    An everywhere-defined primitive; at nonnegative temperatures it is exactly the manuscript's finite-spectrum interaction functional.

    def finiteTemperatureFunctional (ρ eig : ι → ℝ) (hρ : ∀ a, 0 < ρ a)
    (hρsum : ∑ a, ρ a = 1) (p : OverlapPath) (t : ℝ) : ℝ :=
…

    Mentions: OAI.InvariantIsing.OverlapPath

  3. theorem OAI.InvariantIsing.finiteTemperatureFunctional_eq line 44
  4. theorem OAI.InvariantIsing.finiteTemperatureFunctional_zero line 50
  5. theorem OAI.InvariantIsing.continuous_finiteTemperatureFunctional line 55
  6. theorem OAI.InvariantIsing.hasDerivAt_finiteTemperatureFunctional line 61
  7. lemma OAI.InvariantIsing.finiteTemperatureFunctional_modulus line 70