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authorJaron Kent-Dobias <jaron@kent-dobias.com>2023-02-06 17:05:47 +0100
committerJaron Kent-Dobias <jaron@kent-dobias.com>2023-02-06 17:05:47 +0100
commit49799190a6d089ba58758c76b7a2194934af2de5 (patch)
treeb3a6ebab1afd773358bf2bccb9bae058630ba996 /IsingScalingFunction.wl
parentf544ee4176410f276ef425b60a1670ae4dcfa7b5 (diff)
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Added an inverse coordinate function.
Diffstat (limited to 'IsingScalingFunction.wl')
-rw-r--r--IsingScalingFunction.wl20
1 files changed, 14 insertions, 6 deletions
diff --git a/IsingScalingFunction.wl b/IsingScalingFunction.wl
index 29370eb..b119b9f 100644
--- a/IsingScalingFunction.wl
+++ b/IsingScalingFunction.wl
@@ -99,7 +99,7 @@ Ghs := {
Around[-1.04 10^7, 0.01 10^7]
}
-Data[2] = <|
+Data[2] = Rationalize[#, 10^-20] & /@ <|
"θ0" -> 1.148407773492004`,
"θYL" -> 0.9896669889911205`,
"CYL" -> -0.172823989504767`,
@@ -107,7 +107,7 @@ Data[2] = <|
"gs" -> {0.37369093055254343`, -0.021636313152585823`}
|>
-Data[3] = <|
+Data[3] = Rationalize[#, 10^-20] & /@ <|
"θ0" -> 1.2542120477507488`,
"θYL" -> 0.6020557328641167`,
"CYL" -> -0.38566364361428684`,
@@ -115,7 +115,7 @@ Data[3] = <|
"gs" -> {0.4483788209731592`, -0.022032295172535358`, 0.00022200608228654115`}
|>
-Data[4] = <|
+Data[4] = Rationalize[#, 10^-20] & /@ <|
"θ0" -> 1.3164928721109121`,
"θYL" -> 0.6400189996493497`,
"CYL" -> -0.3563974694580203`,
@@ -123,7 +123,7 @@ Data[4] = <|
"gs" -> {0.4410742751152714`, -0.034817777358116885`, 0.000678172648789985`, -0.00004305140578834467`}
|>
-Data[5] = <|
+Data[5] = Rationalize[#, 10^-20] & /@ <|
"θ0" -> 1.3403205742656135`,
"θYL" -> 0.6238113973493433`,
"CYL" -> -0.38002950945224295`,
@@ -131,7 +131,7 @@ Data[5] = <|
"gs" -> {0.44371885415894785`, -0.04609943321005163`, -0.0007458341071947777`, 0.00005966875622885447`, -4.403083529955303`*^-6}
|>
-Data[6] = <|
+Data[6] = Rationalize[#, 10^-20] & /@ <|
"θ0" -> 1.3626103817690176`,
"θYL" -> 0.6462147447024515`,
"CYL" -> -0.35576386594103865`,
@@ -163,6 +163,14 @@ ut[R_, θ_] := R t[θ]
uh[θ0_, gs_][R_, θ_] := R^Δ g[θ0, gs][θ]
+InverseCoordinates[\[Theta]0_, gs_, wp_:20][tn_, hn_] :=
+ ({Exp[logR], \[Theta]0 Tanh[x]} /.
+ FindRoot[{
+ Rationalize[tn, 10^-30] == ut[Exp[logR], \[Theta]0 Tanh[x]],
+ Rationalize[hn, 10^-30] == uh[\[Theta]0, gs][Exp[logR], \[Theta]0 Tanh[x]]
+ }, {{logR, 2}, {x, Sign[hn]/2}}, WorkingPrecision -> wp]) /;
+ NumericQ[tn] && NumericQ[hn]
+
η[θ0_, gs_][θ_] := t[θ] / RealAbs[g[θ0, gs][θ]]^(1 / Δ)
ξ[θ0_, gs_][θ_] := g[θ0, gs][θ] / RealAbs[t[θ]]^Δ
@@ -198,7 +206,7 @@ InverseDerivativeList[n_][f_][x_] := Module[
fp'[xp] D[Pm, xp] - (2 m - 1) fp''[xp] Pm], 1, Range[n - 1]] /.
Derivative[m_][fp][xp] :> dfs[[m]];
MapIndexed[{Pn, i} \[Function] Pn/dfs[[1]]^(2 i[[1]] - 1), Pns]
- ]
+]
CompositeFunctionDerivativeList[G_, F_, X_, FSupp_:(0&)][m_, θ_] := Module[
{ ds, dF, df, fp },