Through the following code, we generate Tp1:

`In[1]:= tempPV = ( 3 \[Pi]^(2/3) + 6 6^(2/3) P \[Pi] V^(2/3) - 6^(2/3) V^( 2/3) (-3 + Sqrt[ 9 + (4 6^(2/3) \[Pi]^(4/3) q^2)/( V^(4/3) \[Beta]^2)]) \[Beta]^2 + 3 6^(2/3) V^( 2/3) \[Beta]^2 Log[ 1/6 (3 + Sqrt[ 9 + (4 6^(2/3) \[Pi]^(4/3) q^2)/(V^(4/3) \[Beta]^2)])])/( 6 6^(1/3) \[Pi]^(4/3) V^(1/3)); In[2]:= \[Beta]in = 0.01; \[Beta]fi = 100; \[Beta]st = 0.005; Table[ xlog[\[Beta]] = Log[10, \[Beta]] , {\[Beta], \[Beta]in, \[Beta]fi, \[Beta]st}]; In[6]:= parap1 = {q -> 0.1, V4 -> 5000}; parap2 = {T2 -> 15, q -> 0.1, V2 -> 10000}; parap4 = {T4 -> 5, q -> 0.1, V4 -> 5000}; In[9]:= Table[ pressp2[\[Beta]] = P /. Solve[(tempPV - T2 == 0) /. V -> V2 /. parap2, P][[1]];(*p1= p2*) pressp4[\[Beta]] = P /. Solve[(tempPV - T4 == 0) /. V -> V4 /. parap4, P][[1]];(*p3= p4*) Tp1[\[Beta]] = T1 /. Solve[(tempPV - T1 == 0) /. V -> V4 /. parap1 /. P -> pressp2[\[Beta]], T1][[1]]; , {\[Beta], \[Beta]in, \[Beta]fi, \[Beta]st}]; In[10]:= mi = Min[Table[Tp1[\[Beta]], {\[Beta], \[Beta]in, \[Beta]fi, \[Beta]st}]] ma = Max[Table[ Tp1[\[Beta]], {\[Beta], \[Beta]in, \[Beta]fi, \[Beta]st}]] Out[10]= 11.9083 Out[11]= 11.9083 In[12]:= ListPlot[ Table[{xlog[\[Beta]], Tp1[\[Beta]]}, {\[Beta], \[Beta]in, \[Beta]fi, \[Beta]st}], ScalingFunctions -> {Rescale[#, {mi, ma}, {0.`, 1.`}] &, Rescale[#, {0.`, 1.`}, {mi, ma}] &}, Joined -> True, Frame -> True, FrameStyle -> Black, BaseStyle -> {FontSize -> 14, PrintPrecision -> 11}, FrameLabel -> {"\!\(\*SubscriptBox[\(log\), \(10\)]\) (\[Beta])", "\!\(\*SubscriptBox[\(T\), \(1\)]\)"}, RotateLabel -> False, PlotStyle -> {Blue, Thickness[0.006]}, PlotRange -> {{-2, 2}, {mi, ma}}, Axes -> None, AspectRatio -> 0.8, ImageSize -> 400, FrameTicks -> {{ticks, None}, {Automatic, None}}] `

The result is the following plot:

As it is clear there is a strange fluctuation for $ log_{10}^{\beta}=1-2$ . As it should be a smooth decreasing plot, what is the origin of these fluctuations? How to fix this possibly numerical error?