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feat: freeEnergy jointly AnalyticOnNhd ℝ _ Set.univ (§18.6 capstone, Issue #1499) #1532

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phasetr merged 2 commits into from
May 2, 2026
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feat: freeEnergy jointly AnalyticOnNhd ℝ _ Set.univ (§18.6 capstone, Issue #1499) #1532

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feat: freeEnergy jointly AnalyticOnNhd over Set.univ (§18.6 capstone,…
phasetr May 2, 2026
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feat: freeEnergy jointly AnalyticOnNhd over Set.univ (§18.6 capstone,…
phasetr May 2, 2026
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20 changes: 20 additions & 0 deletions IsingModel/ClusterExpansion.lean
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Original file line number Diff line number Diff line change
Expand Up @@ -4795,4 +4795,24 @@ theorem freeEnergy_analyticAt_joint
unfold freeEnergy
exact analyticAt_const.mul h_log

/-- **Partition function jointly `AnalyticOnNhd ℝ` over `Set.univ`**
(§18.6 extension): global form of `partitionFunction_analyticAt_joint`. -/
theorem partitionFunction_analyticOnNhd_joint
{ι : Type*} [Fintype ι] [DecidableEq ι]
(G : SimpleGraph ι) [Fintype G.edgeSet] :
AnalyticOnNhd ℝ
(fun p : ℝ × ℝ × ℝ => partitionFunction G ⟨p.2.1, p.2.2, p.1⟩)
Set.univ :=
fun ⟨β, J, h⟩ _ => partitionFunction_analyticAt_joint G β J h

/-- **Free energy jointly `AnalyticOnNhd ℝ` over `Set.univ`** (§18.6
capstone, jointly): global form of `freeEnergy_analyticAt_joint`. -/
theorem freeEnergy_analyticOnNhd_joint
{ι : Type*} [Fintype ι] [DecidableEq ι]
(G : SimpleGraph ι) [Fintype G.edgeSet] :
AnalyticOnNhd ℝ
(fun p : ℝ × ℝ × ℝ => freeEnergy G ⟨p.2.1, p.2.2, p.1⟩)
Set.univ :=
fun ⟨β, J, h⟩ _ => freeEnergy_analyticAt_joint G β J h

end IsingModel