Fixes and cleaning of example file.

2 files changed, 8632 insertions, 13733 deletions

diff --git a/IsingScalingFunction.wl b/IsingScalingFunction.wl
index 8545567..4069a5d 100644
--- a/IsingScalingFunction.wl
+++ b/IsingScalingFunction.wl
@@ -25,6 +25,9 @@ DScriptFPlusMinusDξList::usage =
 DScriptF0DηList::usage =
   "DScriptF0DηList computes the first m derivatives of the scaling function F_0."
 
+DScriptF0Dη::usage =
+  "DScriptF0Dη computes the mth derivative of the scaling function F_0."
+
 DScriptMCasDξList::usage = "Computes the first m derivatives of the scaling function M given by Caselle et al."
 
 uf::usage = "uf computes the singular free energy u_f."
@@ -45,6 +48,8 @@ PrepareArgument::usage = "Converts scaling function data into appropriate argume
 
 θ0Cas::usage = ""
 
+h0Cas::usage = ""
+
 gsCas::usage = ""
 
 Φs::usage = ""
@@ -252,7 +257,7 @@ DScriptF0Dη[params__][m_, θ_] := Last[DScriptF0DηList[params][m, θ]]
 
 DufDut[θ0_, θYL_, B_, C0_, CYL_, Gs_, gs_][m_][R_, θ_] := m! RealAbs[uh[θ0, gs][R, θ]]^(2 / Δ - m / Δ) DScriptF0Dη[θ0, θYL, B, C0, CYL, Gs, gs][m, θ] + Log[uh[θ0, gs][R, θ]^2] / (8 π Δ) Derivative[m][Function[utp, utp^2]][ut[R, θ]]
 
-DufDuh[θ0_, θYL_, B_, C0_, CYL_, Gs_, gs_][m_][R_, θ_] := m! RealAbs[ut[R, θ]]^(2-m Δ) DScriptFPlusMinusDξ[θ0, θYL, B, C0, CYL, Gs, gs][m, θ] + Derivative[m][Identity][θ] ut[R, θ]^2 / (8 π) Log[ut[R, θ]^2]
+DufDuh[θ0_, θYL_, B_, C0_, CYL_, Gs_, gs_][m_][R_, θ_] := m! RealAbs[ut[R, θ]]^(2-m Δ) DScriptFPlusMinusDξ[θ0, θYL, B, C0, CYL, Gs, gs][m, θ] + Derivative[m][1&][θ] ut[R, θ]^2 / (8 π) Log[ut[R, θ]^2]
 
 ruleB[θ0_, gs_] := (2 * OverlineS / π) * (- g[θ0, gs]'[θ0] / t[θ0]^Δ)
 
@@ -265,8 +270,8 @@ h0Cas := a b ρ /. {
     b -> (-c4/c2^3)^(1/2),
     ρ -> 2.00881
   } /. {
-    c2->Ghs[[3]]2!,
-    c4->Ghs[[5]]["Value"]4!
+    c2->Ghs[[3]] 2!,
+    c4->Ghs[[5]]["Value"] 4!
   }
 
 gsCas := h0Cas * {
diff --git a/IsingScalingFunctionExamples.nb b/IsingScalingFunctionExamples.nb
index 1eda301..c0d868d 100644
--- a/IsingScalingFunctionExamples.nb
+++ b/IsingScalingFunctionExamples.nb
@@ -10,10 +10,10 @@
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+CellTagsIndexPosition[    613248,      11890]
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+         "Effects" -> {
+          "Highlight" -> {"ratio" -> 2}, "HighlightPoint" -> {"ratio" -> 2}, 
+           "Droplines" -> {
+            "freeformCursorMode" -> True, 
+             "placement" -> {"x" -> "All", "y" -> "None"}}}}, 
+       "DefaultMeshStyle" -> AbsolutePointSize[6], "ScalingFunctions" -> 
+       None}, DisplayFunction -> Identity, DisplayFunction -> Identity, 
+     Ticks -> {Automatic, 
+       Charting`ScaledTicks[{Log, Exp}, {Log, Exp}, "Nice", WorkingPrecision -> 
+        MachinePrecision, RotateLabel -> 0]}, 
+     AxesOrigin -> {0, -4.225253979208682}, FrameTicks -> {{
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+         MachinePrecision, RotateLabel -> 0], 
+        Charting`ScaledFrameTicks[{Log, Exp}]}, {Automatic, Automatic}}, 
+     GridLines -> {None, None}, DisplayFunction -> Identity, 
+     PlotRangePadding -> {{
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+        Scaled[0.02]}, {
+        Scaled[0.05], 
+        Scaled[0.05]}}, PlotRangeClipping -> True, ImagePadding -> All, 
+     DisplayFunction -> Identity, 
+     Method -> {
+      "DefaultBoundaryStyle" -> Automatic, 
+       "DefaultGraphicsInteraction" -> {
+        "Version" -> 1.2, "TrackMousePosition" -> {True, False}, 
+         "Effects" -> {
+          "Highlight" -> {"ratio" -> 2}, "HighlightPoint" -> {"ratio" -> 2}, 
+           "Droplines" -> {
+            "freeformCursorMode" -> True, 
+             "placement" -> {"x" -> "All", "y" -> "None"}}}}, 
+       "DefaultMeshStyle" -> AbsolutePointSize[6], "ScalingFunctions" -> None,
+        "ClippingRange" -> {{{-1.999999918367347, 
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+        7.693451190080213}}, {{-1.999999918367347, 
+        1.999999918367347}, {-3.597953707140854, 7.693451190080213}}}}, 
+     DisplayFunction -> Identity, AspectRatio -> 
+     NCache[GoldenRatio^(-1), 0.6180339887498948], Axes -> {True, True}, 
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+       FormBox[
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+         Exp[
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+         Exp[
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+     Frame -> {{False, False}, {False, False}}, 
+     FrameLabel -> {{None, None}, {None, None}}, 
+     FrameTicks -> {{Automatic, Automatic}, {Automatic, Automatic}}, 
+     GridLines -> {None, None}, GridLinesStyle -> Directive[
+       GrayLevel[0.5, 0.4]], LabelStyle -> GrayLevel[0], 
+     Method -> {
+      "DefaultBoundaryStyle" -> Automatic, 
+       "DefaultGraphicsInteraction" -> {
+        "Version" -> 1.2, "TrackMousePosition" -> {True, False}, 
+         "Effects" -> {
+          "Highlight" -> {"ratio" -> 2}, "HighlightPoint" -> {"ratio" -> 2}, 
+           "Droplines" -> {
+            "freeformCursorMode" -> True, 
+             "placement" -> {"x" -> "All", "y" -> "None"}}}}, 
+       "DefaultMeshStyle" -> AbsolutePointSize[6], "ScalingFunctions" -> 
+       None}, PlotRange -> {All, All}, PlotRangeClipping -> True, 
+     PlotRangePadding -> {{Automatic, Automatic}, {Automatic, Automatic}}, 
+     Ticks -> {Automatic, Automatic}}], 
+   FormBox[
+    FormBox[
+     TemplateBox[{
+      "\"\\!\\(\\*SuperscriptBox[\\(10\\), \\(-1\\)]\\)\"", 
+       "\"\\!\\(\\*SuperscriptBox[\\(10\\), \\(-2\\)]\\)\"", 
+       "\"\\!\\(\\*SuperscriptBox[\\(10\\), \\(-3\\)]\\)\"", 
+       "\"\\!\\(\\*SuperscriptBox[\\(10\\), \\(-4\\)]\\)\""}, "LineLegend", 
+      DisplayFunction -> (FormBox[
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+         StyleBox[
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+           TagBox[
+            GridBox[{{
+               StyleBox["h", {
+                 GrayLevel[0], FontFamily -> "Arial"}, Background -> 
+                Automatic, StripOnInput -> False]}, {
+               TagBox[
+                GridBox[{{
+                   TagBox[
+                    GridBox[{{
+                    GraphicsBox[{{
+                    Directive[
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+                    Directive[
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+                    GrayLevel[0]]], 
+                    PointSize[0.5], 
+                    Opacity[1.], 
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+                    AbsoluteThickness[1.6]], {
+                    LineBox[{{0, 10}, {20, 10}}]}}, {
+                    Directive[
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+                    Directive[
+                    Opacity[0.3], 
+                    GrayLevel[0]]], 
+                    PointSize[0.5], 
+                    Opacity[1.], 
+                    RGBColor[0.368417, 0.506779, 0.709798], 
+                    AbsoluteThickness[1.6]], {}}}, AspectRatio -> Full, 
+                    ImageSize -> {20, 10}, PlotRangePadding -> None, 
+                    ImagePadding -> Automatic, 
+                    BaselinePosition -> (Scaled[0.1] -> Baseline)], #}, {
+                    GraphicsBox[{{
+                    Directive[
+                    EdgeForm[
+                    Directive[
+                    Opacity[0.3], 
+                    GrayLevel[0]]], 
+                    PointSize[0.5], 
+                    Opacity[1.], 
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+                    AbsoluteThickness[1.6]], {
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+                    Directive[
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+                    GrayLevel[0]]], 
+                    PointSize[0.5], 
+                    Opacity[1.], 
+                    RGBColor[0.880722, 0.611041, 0.142051], 
+                    AbsoluteThickness[1.6]], {}}}, AspectRatio -> Full, 
+                    ImageSize -> {20, 10}, PlotRangePadding -> None, 
+                    ImagePadding -> Automatic, 
+                    BaselinePosition -> (Scaled[0.1] -> Baseline)], #2}, {
+                    GraphicsBox[{{
+                    Directive[
+                    EdgeForm[
+                    Directive[
+                    Opacity[0.3], 
+                    GrayLevel[0]]], 
+                    PointSize[0.5], 
+                    Opacity[1.], 
+                    RGBColor[0.560181, 0.691569, 0.194885], 
+                    AbsoluteThickness[1.6]], {
+                    LineBox[{{0, 10}, {20, 10}}]}}, {
+                    Directive[
+                    EdgeForm[
+                    Directive[
+                    Opacity[0.3], 
+                    GrayLevel[0]]], 
+                    PointSize[0.5], 
+                    Opacity[1.], 
+                    RGBColor[0.560181, 0.691569, 0.194885], 
+                    AbsoluteThickness[1.6]], {}}}, AspectRatio -> Full, 
+                    ImageSize -> {20, 10}, PlotRangePadding -> None, 
+                    ImagePadding -> Automatic, 
+                    BaselinePosition -> (Scaled[0.1] -> Baseline)], #3}, {
+                    GraphicsBox[{{
+                    Directive[
+                    EdgeForm[
+                    Directive[
+                    Opacity[0.3], 
+                    GrayLevel[0]]], 
+                    PointSize[0.5], 
+                    Opacity[1.], 
+                    RGBColor[0.922526, 0.385626, 0.209179], 
+                    AbsoluteThickness[1.6]], {
+                    LineBox[{{0, 10}, {20, 10}}]}}, {
+                    Directive[
+                    EdgeForm[
+                    Directive[
+                    Opacity[0.3], 
+                    GrayLevel[0]]], 
+                    PointSize[0.5], 
+                    Opacity[1.], 
+                    RGBColor[0.922526, 0.385626, 0.209179], 
+                    AbsoluteThickness[1.6]], {}}}, AspectRatio -> Full, 
+                    ImageSize -> {20, 10}, PlotRangePadding -> None, 
+                    ImagePadding -> Automatic, 
+                    BaselinePosition -> (Scaled[0.1] -> Baseline)], #4}}, 
+                    GridBoxAlignment -> {
+                    "Columns" -> {Center, Left}, "Rows" -> {{Baseline}}}, 
+                    AutoDelete -> False, 
+                    GridBoxDividers -> {
+                    "Columns" -> {{False}}, "Rows" -> {{False}}}, 
+                    GridBoxItemSize -> {
+                    "Columns" -> {{All}}, "Rows" -> {{All}}}, 
+                    GridBoxSpacings -> {
+                    "Columns" -> {{0.5}}, "Rows" -> {{0.8}}}], "Grid"]}}, 
+                 GridBoxAlignment -> {
+                  "Columns" -> {{Left}}, "Rows" -> {{Top}}}, AutoDelete -> 
+                 False, GridBoxItemSize -> {
+                  "Columns" -> {{Automatic}}, "Rows" -> {{Automatic}}}, 
+                 GridBoxSpacings -> {"Columns" -> {{1}}, "Rows" -> {{0}}}], 
+                "Grid"]}}, GridBoxAlignment -> {"Columns" -> {{Center}}}, 
+             AutoDelete -> False, 
+             GridBoxItemSize -> {
+              "Columns" -> {{Automatic}}, "Rows" -> {{Automatic}}}, 
+             GridBoxSpacings -> {
+              "Columns" -> {{Automatic}}, "Rows" -> {{Automatic}}}], "Grid"], 
+           Alignment -> Left, AppearanceElements -> None, 
+           ImageMargins -> {{5, 5}, {5, 5}}, ImageSizeAction -> 
+           "ResizeToFit"], LineIndent -> 0, StripOnInput -> False], {
+          GrayLevel[0], FontFamily -> "Arial"}, Background -> Automatic, 
+         StripOnInput -> False], TraditionalForm]& ), 
+      InterpretationFunction :> (RowBox[{"LineLegend", "[", 
+         RowBox[{
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+             RowBox[{
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+                 RowBox[{
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