I’m not sure if the definitions you posted are different from the ones used in your plot, or you have lingering definitions that are interfering, but the plot I get from your code is slightly different than the one you show.

```
Z1D((Beta)_, (Xi)_, (Theta)_) = (1/(Xi) (2/(Beta)^2 -
1) + (((Theta) Exp(-(Beta)))/2 - 1/2) +
Sum(((-(Beta))^n (Xi)^(n/2))/n! HurwitzZeta(-(n/2),
1 + 1/(Xi)), {n, 1, 80}));
Cv0((Beta)_, (Xi)_) = (Beta)^2 D(
Log(Z1D((Beta), (Xi), 1)), {(Beta), 2});
CSS((Beta)_, a_) =
Cv0((Beta), 18) +
a/2 (Beta)^2 D((Beta)^2/Z1D((Beta), 18, 1) D(
Z1D((Beta), 18, 1), {(Beta), 2}) -
Log(Z1D((Beta), 18, 1))^2, {(Beta), 2});
Quiet@Plot({
CSS((Beta), 0),
CSS((Beta), 5/100),
CSS((Beta), 1/10),
CSS((Beta), 5/10)
},
{(Beta), 0, 5},
WorkingPrecision -> 50,
PlotPoints -> 100,
MaxRecursion -> 3,
PlotLegends -> "Expressions"
)
```

I think that setting `MaxRecursion`

artificially low (to 1) might be responsible for the gaps you see in your plot. I have it set to 3 here. J.M.’s suggestion of `Exclusions -> None`

also works even with `MaxRecursion -> 1`

.

Also, I don’t know enough about the Mathematics of your functions to know for sure, but it sure looks like the result is complex beyond about 4.5 depending on the exact function.

```
Block({$MaxExtraPrecision = 500},
N({CSS(9/2, 0), CSS(9/2, 5/100), CSS(9/2, 1/10), CSS(9/2, 5/10)}, 50)
)
```

$-79699.364150898969209802685927039062671148814585580$

$ 8.35688067895158097516109070604051

17173041706645372times 10^7+12519.146845612096555038077041258063228049288586

i$$1.6721731294318251847243161680673727340875456210533times

10^8+25038.29369122419311007615408251612645609857717

i$$8.3640536217251618823899729477739452329445740578499times

10^8+125191.46845612096555038077041258063228049288586 i$

I’m using `Block({$MaxExtraPrecision = 500}, ...)`

to tell Mathematica that it can use a precision up to 550 while evaluating the numbers in order to ensure that it returns numbers with a precision of at least 50. Without the `Block`

, I run into a warning that says `$MaxExtraPrecision = 50 reach while evaluating`

. Fortunately, even without the `Block`

the numbers are basically the same, but they’re nowhere near a precision of 50. In fact, their precision is around 10.

For small values of $beta$, the precision remains high. But as the value of $beta$ increases, it seems like the precision diminishes rapidly unless you allow Mathematica to use extra precision. This doesn’t seem to affect the plot, but I thought it was interesting so I wanted to mention it. It also leads me to believe that Mathematica isn’t mistaken when it says those high $beta$ functions are complex.