diff options
| -rw-r--r-- | IsingScalingFunctionExamples.nb | 242 |
1 files changed, 197 insertions, 45 deletions
diff --git a/IsingScalingFunctionExamples.nb b/IsingScalingFunctionExamples.nb index 5327e14..3d355ca 100644 --- a/IsingScalingFunctionExamples.nb +++ b/IsingScalingFunctionExamples.nb @@ -10,10 +10,10 @@ NotebookFileLineBreakTest NotebookFileLineBreakTest NotebookDataPosition[ 158, 7] -NotebookDataLength[ 548992, 10652] -NotebookOptionsPosition[ 543628, 10559] -NotebookOutlinePosition[ 544025, 10575] -CellTagsIndexPosition[ 543982, 10572] +NotebookDataLength[ 554300, 10804] +NotebookOptionsPosition[ 548009, 10695] +NotebookOutlinePosition[ 548406, 10711] +CellTagsIndexPosition[ 548363, 10708] WindowFrame->Normal*) (* Beginning of Notebook Content *) @@ -3965,14 +3965,14 @@ FontSlant->\\\"Italic\\\"], RowBox[{RowBox[{RowBox[{\\\"-\\\", \\\"1\\\"}], \ 3.887183948573832*^9, 3.893237432392331*^9}, CellLabel->"Out[16]=",ExpressionUUID->"e027c86a-5f73-49af-9682-15a84fa4ac67"] }, Open ]] -}, Open ]], +}, Closed]], Cell[CellGroupData[{ Cell["Plotting as functions of scaling invariants", "Section", CellChangeTimes->{{3.887175601990197*^9, 3.887175605174004*^9}, { - 3.887175638310907*^9, - 3.887175648462943*^9}},ExpressionUUID->"af69f70f-b3b9-4794-8398-\ + 3.887175638310907*^9, 3.887175648462943*^9}, {3.893240667249942*^9, + 3.893240669191936*^9}},ExpressionUUID->"af69f70f-b3b9-4794-8398-\ 01134650a149"], Cell[BoxData[{ @@ -7366,13 +7366,22 @@ StyleBox[\\\"|\\\",FontSlant->\\\"Italic\\\"], RowBox[{RowBox[{\\\"-\\\", \ 3.893237610747847*^9, {3.8932377310303297`*^9, 3.893237737874032*^9}}, CellLabel->"Out[48]=",ExpressionUUID->"5632f44e-d2ee-4570-afa0-630f5721d24c"] }, Open ]] -}, Open ]], +}, Closed]], Cell[CellGroupData[{ -Cell["Plotting as functions of control variables", "Section", +Cell[TextData[{ + "Applications: plotting as functions of control variables (", + StyleBox["t", + FontSlant->"Italic"], + " and ", + StyleBox["h", + FontSlant->"Italic"], + ")" +}], "Section", CellChangeTimes->{{3.887175666126995*^9, 3.887175672719225*^9}, - 3.8871757098402243`*^9},ExpressionUUID->"7bcdac80-37e1-4f66-bc64-\ + 3.8871757098402243`*^9, {3.893240714208487*^9, + 3.8932407443131866`*^9}},ExpressionUUID->"7bcdac80-37e1-4f66-bc64-\ b0d2db5bf4c3"], Cell[BoxData[{ @@ -7395,6 +7404,32 @@ Cell[BoxData[{ Cell[CellGroupData[{ +Cell["Entropy", "Subsection", + CellChangeTimes->{{3.893240903148159*^9, + 3.893240903699958*^9}},ExpressionUUID->"732869ab-e280-4316-b799-\ +ffab64c308f3"], + +Cell[TextData[{ + "In this plot, we show ", + Cell[BoxData[ + FormBox[ + FractionBox[ + RowBox[{"\[PartialD]", + SubscriptBox["u", "f"]}], + RowBox[{"\[PartialD]", + SubscriptBox["u", "t"]}]], TraditionalForm]], + FormatType->TraditionalForm,ExpressionUUID-> + "20c22e44-ae22-4cf1-ba9e-ec412d2155ac"], + ", which is the singular part of the entropy (modulo a constant analytic \ +factor) near the transition." +}], "Text", + CellChangeTimes->{{3.893240788042069*^9, 3.89324084285141*^9}, { + 3.893240875195952*^9, + 3.893240882915715*^9}},ExpressionUUID->"22825260-2ae9-4101-a1f7-\ +3f6b1bfde9fc"], + +Cell[CellGroupData[{ + Cell[BoxData[ RowBox[{"Plot", "[", RowBox[{ @@ -8278,10 +8313,39 @@ I5knh+jg5ECZ1thLQ7042gfvr3Swc9C7syBDQ1bmjLPCPxh6wnpEm5VpiPZu CellChangeTimes->{3.8871885224783792`*^9, 3.8932376275906477`*^9, 3.893237839180531*^9, 3.893237876356636*^9}, CellLabel->"Out[52]=",ExpressionUUID->"f282764d-6683-431e-bd66-aff690b1329a"] +}, Open ]] }, Open ]], Cell[CellGroupData[{ +Cell["Specific heat", "Subsection", + CellChangeTimes->{{3.893240903148159*^9, + 3.8932409167324743`*^9}},ExpressionUUID->"91682356-0150-4742-8ad7-\ +87c14223ec68"], + +Cell[TextData[{ + "In this plot, we show ", + Cell[BoxData[ + FormBox[ + FractionBox[ + RowBox[{ + SuperscriptBox["\[PartialD]", "2"], + SubscriptBox["u", "f"]}], + RowBox[{"\[PartialD]", + SuperscriptBox[ + SubscriptBox["u", "t"], "2"]}]], TraditionalForm]], + FormatType->TraditionalForm,ExpressionUUID-> + "a889c51d-cced-4075-b076-eae0732091de"], + ", which is the singular part of the specific heat (modulo a constant \ +analytic factor) near the transition." +}], "Text", + CellChangeTimes->{{3.893240788042069*^9, 3.89324084285141*^9}, { + 3.893240875195952*^9, 3.893240882915715*^9}, {3.893240920042145*^9, + 3.893240927292811*^9}},ExpressionUUID->"6d8da3cb-bbd1-4fe2-a26c-\ +2969b50861eb"], + +Cell[CellGroupData[{ + Cell[BoxData[ RowBox[{"Plot", "[", RowBox[{ @@ -9013,10 +9077,49 @@ gSdjuir9R3nQ2tJ0hmJC4FL+9GNS4zywypV499iUQHT0YFT95IHyUHyq2SkC 3.887187744969038*^9, 3.8871877776872168`*^9, 3.8871880220364237`*^9, 3.893237910849724*^9}, CellLabel->"Out[53]=",ExpressionUUID->"632547c6-cf8a-4755-9e26-5f9a8c901698"] +}, Open ]] }, Open ]], Cell[CellGroupData[{ +Cell["Magnetization", "Subsection", + CellChangeTimes->{{3.893240903148159*^9, 3.8932409167324743`*^9}, { + 3.893240952846768*^9, + 3.893240954869104*^9}},ExpressionUUID->"b265c475-5c2a-4729-88fe-\ +bb9de99d3c77"], + +Cell[TextData[{ + "In this plot, we show ", + Cell[BoxData[ + FormBox[ + FractionBox[ + RowBox[{"\[PartialD]", + SubscriptBox["u", "f"]}], + RowBox[{"\[PartialD]", + SubscriptBox["u", "h"]}]], TraditionalForm]], + FormatType->TraditionalForm,ExpressionUUID-> + "9ccc58f9-7198-4f0c-b1fc-1a083a734169"], + ", which is the singular part of the magnetization (modulo a constant \ +analytic factor) near the transition. Notice here, as in all plots using this \ +library, that ", + Cell[BoxData[ + FormBox[ + RowBox[{"t", "\[Proportional]", + RowBox[{ + SubscriptBox["T", "c"], "-", "T"}]}], TraditionalForm]], + FormatType->TraditionalForm,ExpressionUUID-> + "6a836779-b628-479e-87a4-c2772a03c8a2"], + " (the negative of the usual sense) following conventions in high energy \ +physics." +}], "Text", + CellChangeTimes->{{3.893240788042069*^9, 3.89324084285141*^9}, { + 3.893240875195952*^9, 3.893240882915715*^9}, {3.893240920042145*^9, + 3.893240927292811*^9}, {3.893240957814611*^9, + 3.8932410410866423`*^9}},ExpressionUUID->"78afd124-f9bb-430d-875b-\ +072cdcafc777"], + +Cell[CellGroupData[{ + Cell[BoxData[ RowBox[{"Plot", "[", RowBox[{ @@ -9800,10 +9903,42 @@ MgVUvd0rD+SQweXnBfMbGxSoFwtmfvOP////Ay9Djxqx5JLhfyEsbYw= 3.887187949227336*^9}, {3.8871879838276787`*^9, 3.887188010158411*^9}, 3.8871882575514183`*^9, 3.893237964294105*^9}, CellLabel->"Out[54]=",ExpressionUUID->"18837f4b-03ee-4fc9-b362-36801a1721f3"] 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