From b8fc822e94382883c8a772344f3d8f77686a6282 Mon Sep 17 00:00:00 2001 From: Jaron Kent-Dobias Date: Tue, 7 Mar 2023 15:32:39 +0100 Subject: Fixes and cleaning of example file. --- IsingScalingFunction.wl | 11 +- IsingScalingFunctionExamples.nb | 26568 +++++++++++++++----------------------- 2 files changed, 10739 insertions(+), 15840 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 @@ NotebookFileLineBreakTest NotebookFileLineBreakTest NotebookDataPosition[ 158, 7] -NotebookDataLength[ 944999, 17080] -NotebookOptionsPosition[ 934897, 16909] -NotebookOutlinePosition[ 935294, 16925] -CellTagsIndexPosition[ 935251, 16922] +NotebookDataLength[ 618512, 11974] +NotebookOptionsPosition[ 612895, 11877] +NotebookOutlinePosition[ 613291, 11893] +CellTagsIndexPosition[ 613248, 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0.2125], + AbsoluteThickness[1.6]], + Directive[ + RGBColor[0.40082222609352647`, 0.5220066643438841, 0.85], + AbsoluteThickness[1.6]], + Directive[ + RGBColor[ + 0.9728288904374106, 0.621644452187053, 0.07336199581899142], + AbsoluteThickness[1.6]], + Directive[ + RGBColor[0.736782672705901, 0.358, 0.5030266573755369], + AbsoluteThickness[1.6]], + Directive[ + RGBColor[0.28026441037696703`, 0.715, 0.4292089322474965], + AbsoluteThickness[1.6]]}, "DomainPadding" -> Scaled[0.02], + "PointSizeFunction" -> "SmallPointSize", "RangePadding" -> + Scaled[0.05], "OptimizePlotMarkers" -> True, "OptimizePlotMarkers" -> + True, "CoordinatesToolOptions" -> {"DisplayFunction" -> ({ + Identity[ + Part[#, 1]], + Exp[ + Part[#, 2]]}& ), "CopiedValueFunction" -> ({ + Identity[ + Part[#, 1]], + Exp[ + Part[#, 2]]}& )}}, + PlotRange -> {{0., 14.}, {-4.900657053954936, 15.35666962964508}}, + PlotRangeClipping -> True, PlotRangePadding -> {{ Scaled[0.02], Scaled[0.02]}, { Scaled[0.02], - Scaled[0.02]}}, Ticks -> {Automatic, Automatic}}], + Scaled[0.05]}}, Ticks -> {Automatic, + Charting`ScaledTicks[{Log, Exp}, {Log, Exp}, "Nice", WorkingPrecision -> + 15.954589770191003`, RotateLabel -> 0]}}], FormBox[ FormBox[ - TemplateBox[{"2", "3", "4", "5"}, "LineLegend", - DisplayFunction -> (FormBox[ + TemplateBox[{ + "\"Numerics\"", + "\"Ours (\\!\\(\\*StyleBox[\\\"n\\\",FontSlant->\\\"Italic\\\"]\\) = \ +2)\"", "\"Ours (\\!\\(\\*StyleBox[\\\"n\\\",FontSlant->\\\"Italic\\\"]\\) = \ +6)\"", "\"Casselle \\!\\(\\*StyleBox[\\\"et\\\",FontSlant->\\\"Italic\\\"]\\)\ +\\!\\(\\*StyleBox[\\\" \\\",FontSlant->\\\"Italic\\\"]\\)\\!\\(\\*StyleBox[\\\ +\"al\\\",FontSlant->\\\"Italic\\\"]\\)\\!\\(\\*StyleBox[\\\".\\\",FontSlant->\ +\\\"Italic\\\"]\\)\""}, "PointLegend", DisplayFunction -> (FormBox[ StyleBox[ StyleBox[ PaneBox[ TagBox[ GridBox[{{ - StyleBox["\"n\"", { - GrayLevel[0], FontSize -> 12, FontFamily -> "Arial"}, - Background -> Automatic, StripOnInput -> False]}, { TagBox[ GridBox[{{ - TagBox[ - 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Opacity[1.], RGBColor[0.560181, 0.691569, 0.194885], - AbsoluteThickness[1.6]], {}}}, AspectRatio -> Full, - ImageSize -> {20, 10}, PlotRangePadding -> None, + AbsoluteThickness[1.6]], + PointBox[ + NCache[{ + Scaled[{ + Rational[1, 2], + Rational[1, 2]}]}, { + Scaled[{0.5, 0.5}]}]]}}}, AspectRatio -> Full, + ImageSize -> {10, 10}, PlotRangePadding -> None, ImagePadding -> Automatic, - BaselinePosition -> (Scaled[0.038000000000000006`] -> - Baseline)], #3}, { - GraphicsBox[{{ + 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, + AbsoluteThickness[1.6]], + PointBox[ + NCache[{ + Scaled[{ + Rational[1, 2], + Rational[1, 2]}]}, { + Scaled[{0.5, 0.5}]}]]}}}, AspectRatio -> Full, + ImageSize -> {10, 10}, PlotRangePadding -> None, ImagePadding -> Automatic, - BaselinePosition -> (Scaled[0.038000000000000006`] -> - 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"]}}, + BaselinePosition -> (Scaled[0.1] -> Baseline)], #4}}, GridBoxAlignment -> { - "Columns" -> {{Left}}, "Rows" -> {{Top}}}, AutoDelete -> - False, GridBoxItemSize -> { - "Columns" -> {{Automatic}}, "Rows" -> {{Automatic}}}, - GridBoxSpacings -> {"Columns" -> {{1}}, "Rows" -> {{0}}}], - "Grid"]}}, GridBoxAlignment -> {"Columns" -> {{Center}}}, + "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" -> {{Automatic}}, "Rows" -> {{Automatic}}}], "Grid"], - Alignment -> Left, AppearanceElements -> None, + GridBoxSpacings -> {"Columns" -> {{1}}, "Rows" -> {{0}}}], + "Grid"], Alignment -> Left, AppearanceElements -> None, ImageMargins -> {{5, 5}, {5, 5}}, ImageSizeAction -> "ResizeToFit"], LineIndent -> 0, StripOnInput -> False], { - GrayLevel[0], FontSize -> 12, FontFamily -> "Arial"}, Background -> - Automatic, StripOnInput -> False], TraditionalForm]& ), - InterpretationFunction :> (RowBox[{"LineLegend", "[", + FontFamily -> "Arial"}, Background -> Automatic, StripOnInput -> + False], TraditionalForm]& ), + InterpretationFunction :> (RowBox[{"PointLegend", "[", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"Directive", "[", RowBox[{ - RowBox[{"Opacity", "[", "1.`", "]"}], ",", + RowBox[{"PointSize", "[", "0.012833333333333334`", "]"}], + ",", TemplateBox[<| "color" -> RGBColor[0.368417, 0.506779, 0.709798]|>, @@ -856,7 +639,8 @@ FontSlant->\\\"Italic\\\"], RowBox[{RowBox[{RowBox[{\\\"-\\\", \\\"1\\\"}], \ ",", RowBox[{"Directive", "[", RowBox[{ - RowBox[{"Opacity", "[", "1.`", "]"}], ",", + RowBox[{"PointSize", "[", "0.012833333333333334`", "]"}], + ",", TemplateBox[<| "color" -> RGBColor[0.880722, 0.611041, 0.142051]|>, @@ -865,7 +649,8 @@ FontSlant->\\\"Italic\\\"], RowBox[{RowBox[{RowBox[{\\\"-\\\", \\\"1\\\"}], \ ",", RowBox[{"Directive", "[", RowBox[{ - RowBox[{"Opacity", "[", "1.`", "]"}], ",", + RowBox[{"PointSize", "[", "0.012833333333333334`", "]"}], + ",", TemplateBox[<| "color" -> RGBColor[0.560181, 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