From a6daedd1a445dcd2fd130fb93869fecc0fc39219 Mon Sep 17 00:00:00 2001
From: victor <victor.vanthilt@gmail.com>
Date: Tue, 21 Jan 2025 11:32:24 +0100
Subject: [PATCH] add onsager ising free energy const using high precision
 quadgk

---
 src/models/ising.jl |  2 ++
 test/finalize.jl    | 10 +++++-----
 test/ising.jl       | 18 ++++--------------
 3 files changed, 11 insertions(+), 19 deletions(-)

diff --git a/src/models/ising.jl b/src/models/ising.jl
index d13367c..e0cadb1 100644
--- a/src/models/ising.jl
+++ b/src/models/ising.jl
@@ -1,6 +1,8 @@
 const Ising_βc = log(1.0 + sqrt(2)) / 2.0
 Potts_βc(q) = log(1.0 + sqrt(q))
 
+const f_onsager::BigFloat = -2.10965114460820745966777928351108478082549327543540531781696107967700291143188081390114126499095041781
+
 function classical_ising(β::Number; h=0)
     function σ(i::Int64)
         return 2i - 3
diff --git a/test/finalize.jl b/test/finalize.jl
index b5278ff..84160af 100644
--- a/test/finalize.jl
+++ b/test/finalize.jl
@@ -16,7 +16,7 @@ end
 criterion_f(steps::Int, data) = abs(log(data[end]) * 2.0^(1 - steps))
 
 T = classical_ising_symmetric(Ising_βc)
-fs_onsager = onsager_free_energy(Ising_βc)
+f_onsager = onsager_free_energy(Ising_βc)
 
 # TRG
 @testset "TRG - Ising Model" begin
@@ -30,7 +30,7 @@ fs_onsager = onsager_free_energy(Ising_βc)
 
     fs = lnz * -1 / Ising_βc
 
-    relerror = abs((fs - fs_onsager) / fs_onsager)
+    relerror = abs((fs - f_onsager) / f_onsager)
     @test relerror < 2e-6
 end
 
@@ -46,7 +46,7 @@ end
 
     fs = lnz * -1 / Ising_βc
 
-    relerror = abs((fs - fs_onsager) / fs_onsager)
+    relerror = abs((fs - f_onsager) / f_onsager)
     @test relerror < 6e-8
 end
 
@@ -62,7 +62,7 @@ end
 
     fs = lnz * -1 / Ising_βc
 
-    relerror = abs((fs - fs_onsager) / fs_onsager)
+    relerror = abs((fs - f_onsager) / f_onsager)
     @test relerror < 6e-7
 end
 
@@ -78,6 +78,6 @@ end
 
     fs = lnz * -1 / Ising_βc
 
-    relerror = abs((fs - fs_onsager) / fs_onsager)
+    relerror = abs((fs - f_onsager) / f_onsager)
     @test relerror < 3e-6
 end
diff --git a/test/ising.jl b/test/ising.jl
index ad5ce47..15e28f8 100644
--- a/test/ising.jl
+++ b/test/ising.jl
@@ -3,20 +3,10 @@ println(" Ising Model ")
 println("-------------")
 
 # Onsager solution
-function onsager_integrand(θ, T)
-    k = 1 / sinh(2 / T)^(2)
-    integrand = 1 / (2π) * log(cosh(2 / T)^2 + 1 / k * sqrt(1 + k^2 - 2k * cos(2 * θ)))
-    return integrand
-end
-
-function onsager_free_energy(β)
-    return -(quadgk(θ -> onsager_integrand(θ, 1 / β), 0, π)[1] + log(2) / 2) / β
-end
 
 criterion_f(steps::Int, data) = abs(log(data[end]) * 2.0^(1 - steps))
 
 T = classical_ising_symmetric(Ising_βc)
-fs_onsager = onsager_free_energy(Ising_βc)
 
 # TRG
 @testset "TRG - Ising Model" begin
@@ -30,7 +20,7 @@ fs_onsager = onsager_free_energy(Ising_βc)
 
     fs = lnz * -1 / Ising_βc
 
-    relerror = abs((fs - fs_onsager) / fs_onsager)
+    relerror = abs((fs - f_onsager) / f_onsager)
     @test relerror < 2e-6
 end
 
@@ -46,7 +36,7 @@ end
 
     fs = lnz * -1 / Ising_βc
 
-    relerror = abs((fs - fs_onsager) / fs_onsager)
+    relerror = abs((fs - f_onsager) / f_onsager)
     @test relerror < 6e-8
 end
 
@@ -62,7 +52,7 @@ end
 
     fs = lnz * -1 / Ising_βc
 
-    relerror = abs((fs - fs_onsager) / fs_onsager)
+    relerror = abs((fs - f_onsager) / f_onsager)
     @test relerror < 6e-7
 end
 
@@ -78,6 +68,6 @@ end
 
     fs = lnz * -1 / Ising_βc
 
-    relerror = abs((fs - fs_onsager) / fs_onsager)
+    relerror = abs((fs - f_onsager) / f_onsager)
     @test relerror < 3e-6
 end