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| author | Jaron Kent-Dobias <jaron@kent-dobias.com> | 2023-02-10 17:27:13 +0100 |
|---|---|---|
| committer | Jaron Kent-Dobias <jaron@kent-dobias.com> | 2023-02-10 17:27:13 +0100 |
| commit | 0c9f4d522b557a0c9f1436e80bf666d9d2630592 (patch) | |
| tree | f04b37ed745fbfbd69eaad7788f1e5d1a946c03e | |
| parent | 49799190a6d089ba58758c76b7a2194934af2de5 (diff) | |
| download | paper-0c9f4d522b557a0c9f1436e80bf666d9d2630592.tar.gz paper-0c9f4d522b557a0c9f1436e80bf666d9d2630592.tar.bz2 paper-0c9f4d522b557a0c9f1436e80bf666d9d2630592.zip | |
Some progress.
| -rw-r--r-- | IsingScalingFunction.wl | 39 | ||||
| -rw-r--r-- | IsingScalingFunctionExamples.nb | 8884 |
2 files changed, 8328 insertions, 595 deletions
diff --git a/IsingScalingFunction.wl b/IsingScalingFunction.wl index b119b9f..8545567 100644 --- a/IsingScalingFunction.wl +++ b/IsingScalingFunction.wl @@ -1,5 +1,7 @@ BeginPackage["IsingScalingFunction`"] +InverseCoordinates::usage = "" + g::usage = "g[θ0, gs][θ] gives the Schofield coordinate transformation defined in (14)." ut::usage = "ut[θ] gives the scaling field u_t as a function of Schofield coordinates." @@ -23,6 +25,8 @@ DScriptFPlusMinusDξList::usage = DScriptF0DηList::usage = "DScriptF0DηList computes the first m derivatives 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." DufDut::usage = @@ -39,6 +43,16 @@ Data::usage = "Data[n] gives data from the fit to nth order from Table II." PrepareArgument::usage = "Converts scaling function data into appropriate argument to function interfaces." +θ0Cas::usage = "" + +gsCas::usage = "" + +Φs::usage = "" + +Gls::usage = "" + +Ghs::usage = "" + Begin["Private`"] β := 1/8 @@ -238,17 +252,36 @@ 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] + 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][Identity][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) ruleC0[θ0_, gs_] := Exp[Δ t[θ0]^(Δ - 1) t'[θ0] / (2 OverlineS / π g[θ0, gs]'[θ0]) - t[θ0]^Δ g[θ0, gs]''[θ0] / (4 OverlineS / π g[θ0, gs]'[θ0]^2)] t[θ0]^(1/8) OverlineS / (2 π) * g[θ0, gs]'[θ0] -Unprotect[Derivative] +θ0Cas := Sqrt[1.16951]; +h0Cas := a b ρ /. { + a -> c2^2/c4, + b -> (-c4/c2^3)^(1/2), + ρ -> 2.00881 + } /. { + c2->Ghs[[3]]2!, + c4->Ghs[[5]]["Value"]4! + } +gsCas := h0Cas * { + 1, + -0.222389, + -0.043547, + -0.014809, + -0.007168 + } -Protect[Derivative] +m0Cas := -Ghs[[3]]2! h0Cas + +DScriptMCasDξList[m_, θ_] := CompositeFunctionDerivativeList[ + Identity, Function[θp, m0Cas * θp / RealAbs[θp^2 - 1]^β], ξ[θ0Cas, gsCas] + ][m, θ] End[] diff --git a/IsingScalingFunctionExamples.nb b/IsingScalingFunctionExamples.nb index 7f37ad0..1eda301 100644 --- 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"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, -24.4628263145363}, FrameTicks -> {{ + Charting`ScaledTicks[{Log, Exp}, {Log, Exp}, "Nice", WorkingPrecision -> + MachinePrecision, RotateLabel -> 0], + Charting`ScaledFrameTicks[{Log, Exp}]}, {Automatic, Automatic}}, + GridLines -> {None, None}, DisplayFunction -> Identity, + PlotRangePadding -> {{ + Scaled[0.02], + 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" -> {{{-5.999999755102041, + 5.999999755102041}, {-24.462826314536354`, -8.136370804376675}}, \ +{{-5.999999755102041, + 5.999999755102041}, {-24.462826314536354`, -8.136370804376675}}}}, + DisplayFunction -> Identity, AspectRatio -> + NCache[GoldenRatio^(-1), 0.6180339887498948], Axes -> {True, True}, + AxesLabel -> { + FormBox[ + TagBox[ + "\"\\!\\(\\*StyleBox[\\\"t\\\",FontSlant->\\\"Italic\\\"]\\)\\!\\(\\*\ +StyleBox[\\\" \ +\\\",FontSlant->\\\"Italic\\\"]\\)\\!\\(\\*SuperscriptBox[StyleBox[\\\"h\\\",\ +FontSlant->\\\"Italic\\\"], RowBox[{RowBox[{RowBox[{\\\"-\\\", \\\"1\\\"}], \ +\\\"/\\\", \\\"\[Beta]\\\"}], \\\" \\\", \\\"\[Delta]\\\"}]]\\)\"", HoldForm], + TraditionalForm], + FormBox[ + TagBox[ + "\"| \\!\\(\\*SuperscriptBox[SubscriptBox[\\\"\[ScriptCapitalF]\\\", \ +\\\"0\\\"], RowBox[{\\\"(\\\", StyleBox[\\\"n\\\",FontSlant->\\\"Italic\\\"], \ +\\\")\\\"}]]\\) - \ +\\!\\(\\*SuperscriptBox[SubscriptBox[\\(\[ScriptCapitalF]\\), \\(0\\)], \ +\\((6)\\)]\\) |\"", HoldForm], TraditionalForm]}, + AxesOrigin -> {0, -24.462826314536354`}, + CoordinatesToolOptions -> {"DisplayFunction" -> ({ + Part[#, 1], + Exp[ + Part[#, 2]]}& ), "CopiedValueFunction" -> ({ + Part[#, 1], + Exp[ + Part[#, 2]]}& )}, DisplayFunction :> Identity, + 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], FontSize -> 12}, + 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 -> {{-6, + 6}, {-24.462826314536354`, -8.136370804376675}}, PlotRangeClipping -> + True, PlotRangePadding -> {{ + Scaled[0.02], + Scaled[0.02]}, { + Scaled[0.02], + Scaled[0.02]}}, Ticks -> {Automatic, Automatic}}], + FormBox[ + FormBox[ + TemplateBox[{"2", "3", "4", "5"}, "LineLegend", + DisplayFunction -> (FormBox[ + StyleBox[ + StyleBox[ + PaneBox[ + TagBox[ + GridBox[{{ + StyleBox["\"n\"", { + GrayLevel[0], FontSize -> 12, FontFamily -> "Arial"}, + Background -> Automatic, StripOnInput -> False]}, { + TagBox[ + GridBox[{{ + TagBox[ + GridBox[{{ + GraphicsBox[{{ + Directive[ + EdgeForm[ + Directive[ + Opacity[0.3], + GrayLevel[0]]], + PointSize[0.5], + Opacity[1.], + RGBColor[0.368417, 0.506779, 0.709798], + AbsoluteThickness[1.6]], { + LineBox[{{0, 10}, {20, 10}}]}}, { + Directive[ + EdgeForm[ + 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[0.038000000000000006`] -> + Baseline)], #}, { + GraphicsBox[{{ + Directive[ + EdgeForm[ + Directive[ + Opacity[0.3], + GrayLevel[0]]], + PointSize[0.5], + Opacity[1.], + RGBColor[0.880722, 0.611041, 0.142051], + AbsoluteThickness[1.6]], { + LineBox[{{0, 10}, {20, 10}}]}}, { + Directive[ + EdgeForm[ + Directive[ + Opacity[0.3], + 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[0.038000000000000006`] -> + 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[0.038000000000000006`] -> + 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[0.038000000000000006`] -> + 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"]}}, + 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], FontSize -> 12, FontFamily -> "Arial"}, Background -> + Automatic, StripOnInput -> False], TraditionalForm]& ), + InterpretationFunction :> (RowBox[{"LineLegend", "[", + RowBox[{ + RowBox[{"{", + RowBox[{ + RowBox[{"Directive", "[", + RowBox[{ + RowBox[{"Opacity", "[", "1.`", "]"}], ",", + + TemplateBox[<| + "color" -> RGBColor[0.368417, 0.506779, 0.709798]|>, + "RGBColorSwatchTemplate"], ",", + RowBox[{"AbsoluteThickness", "[", "1.6`", "]"}]}], "]"}], + ",", + RowBox[{"Directive", "[", + RowBox[{ + RowBox[{"Opacity", "[", "1.`", "]"}], ",", + + TemplateBox[<| + "color" -> RGBColor[0.880722, 0.611041, 0.142051]|>, + "RGBColorSwatchTemplate"], ",", + RowBox[{"AbsoluteThickness", "[", "1.6`", "]"}]}], "]"}], + ",", + RowBox[{"Directive", "[", + RowBox[{ + RowBox[{"Opacity", "[", "1.`", "]"}], ",", + + TemplateBox[<| + "color" -> RGBColor[0.560181, 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