Started moving work to script file.

2 files changed, 367 insertions, 265 deletions

diff --git a/new_schofield.nb b/new_schofield.nb
index 84ee0f3..7aafe40 100644
--- a/new_schofield.nb
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diff --git a/schofield.wl b/schofield.wl
new file mode 100644
index 0000000..fdb76e3
--- /dev/null
+++ b/schofield.wl
@@ -0,0 +1,54 @@
+
+BeginPackage["Schofield`"]
+
+β::usage = "Gives the exponent for the magnetization."
+δ::usage = "Exponent."
+α::usage = "Exponent."
+Δ::usage = "Exponent."
+
+$Assumptions = {θc > 0, θi > 0, θc > θi, gC[_] ∈ Reals, B > 0, γ > 0}
+
+β[D_:2] := Piecewise[
+  {
+    {1/8, D == 2},
+    {0.326419, D == 3},
+    {1/2, D == 4},
+    {β, True}
+  }
+]
+
+δ[D_:2] := Piecewise[
+  {
+    {15, D == 2},
+    {4.78984, D == 3},
+    {3, D == 4},
+    {δ, True}
+  }
+]
+
+α[D_:2] := Piecewise[
+  {
+    {0, D == 2},
+    {0.11008, D == 3},
+    {0, D == 4},
+    {α, True}
+  }
+]
+
+Δ[D_:2] := β[D] δ[D]
+
+f[θi_:1][n_][θ_] := (θ / θi)^2 - 1
+g[gC_:gC, θc_:θc][n_][θ_] := (1 - (θ/θc)^2) Sum[gC[i] θ^(2i+1), {i, 0, n}]
+
+I\[ScriptCapitalM]f[γ_][y_] := (1 + (1 + γ x) / x) Exp[-1/x]
+R\[ScriptCapitalM]f[γ_][y_] := (1 - y - γ y) Exp[1/y] ExpIntegralEi[-1/y] / (π y)
+
+R\[ScriptCapitalM][2][γ_, B_, θc_, M0_][θ_] := - M0 (R\[ScriptCapitalM]f[γ][B(θc - θ)] - R\[ScriptCapitalM]f[γ][B(θc + θ)])
+
+eqLow[D_:2][f_, g_][m_] := SeriesCoefficient[
+  R\[ScriptCapitalM][D][γ, B, θc, M0][θ] + f[θ]^β[D] Gl'[g[θ] f[θ]^(-Δ[D])],
+  {θ, θc, m},
+  Assumptions -> Join[$Assumptions, {θ < θc, θ > θi}]
+]
+EndPackage[]
+