ContourPlot fails in a simple equation

Question

I'm very new with Mathematica, and I'm struggling with a very simple problem.

I want to plot this

ContourPlot[Sqrt[-1 + (4 k^2)/(1 + k^2 Z)^2], {k, 0.4, 2500}, {Z, 
  0.001, 1.0}, ClippingStyle -> Automatic, 
 ScalingFunctions -> {"Log", "Log", "Log"}, 
 PlotLegends -> 
  BarLegend[Automatic, All, 
   LabelingFunction -> (Style[NumberForm[#, 3]] &)], PlotPoints -> 20,
  MaxRecursion -> 4, ColorFunction -> "Rainbow", 
 ContourLabels -> False, Contours -> 20, 
 FrameLabel -> {"|\!\(\*OverscriptBox[\(k\), \(~\)]\)|", "Z"}, 
 PlotRange -> {{0.4, 2500}, {.001, 1.2}, {.2, 40}}, 
 ImageSize -> Medium]

Doing that I obtain this

But I know that the function is always <1 when Z>0.5 which is in contrast with the plot.

Zooming (PlotRange -> {{0.4, 5}, {.5, 1.0}, {.2, 40}) I obtain

again wrong, since the function is always less than 1 in this domain.

Decreasing the domain of Z, i obtain something more correct (but i need the full range!)

ContourPlot[Sqrt[-1 + (4 k^2)/(1 + k^2 Z)^2], {k, 0.4, 2500}, {Z, 0.5, 1.0}, ClippingStyle -> Automatic, ScalingFunctions -> {"Log", "Log", "Log"}, PlotLegends -> BarLegend[Automatic, All, LabelingFunction -> (Style[NumberForm[#, 3]] &)], PlotPoints -> 20,MaxRecursion -> 4, ColorFunction -> "Rainbow", ContourLabels -> False, Contours -> 20, FrameLabel -> {"|\!\(\*OverscriptBox[\(k\), \(~\)]\)|", "Z"}, PlotRange -> {{0.4, 5}, {.5, 1.0}, {.2, 40}}, ImageSize -> Medium]

I tried increasing/decreasing the PlotPoints, MaxRecursion, WorkinPrecision and others but I really can't get the clue of the problem!

Can someone solve my problem?

Thank you!

Answer 1

You mistake lies in the LabelingFunction.

You wrote:

BarLegend[Automatic, All, 
  LabelingFunction -> (Style[NumberForm[#, 3]] &)]

but, at the same time your plot range is:

PlotRange -> {{0.4, 2500}, {.001, 1.2}, {.2, 40}}

so you are taking a range from 0.2 to 40 and put it in your Style[NumberForm[#,3]] (this is what the # means). Just remove the LabelingFunction, put it to automatic, or change the plotrange to the maximum of the area you're plotting, and you get this:

In General, it is good to stick with the Automatic options and then add other options as you need them.