How to combine several plots with different $x$ and $y$-axis?

Question

I'm new to Mathematica plots. The following is a small part of my research results:

gthres = 1/3 + (19 - 3 Sqrt[33])^(1/3)/3 + (19 + 3 Sqrt[33])^(1/3)/3;
tthres = Log[gthres];
plot1 = ListLinePlot[{{0.609378, 10}, {0.609379, 8}, {0.609395, 
    6}, {0.610285, 4}, {0.61073, 3.8}, {0.611392, 3.6}, {0.612376, 
    3.4}, {0.613835, 3.2}, {0.615994, 3}, {0.619176, 2.8}, {0.62384, 
    2.6}, {0.630628, 2.4}, {0.640412, 2.2}, {0.654347, 2}, {0.663323, 
    1.9}, {0.673925, 1.8}, {0.686401, 1.7}, {0.70103, 1.6}, {0.718126,
     1.5}, {0.738047, 1.4}, {0.761207, 1.3}, {0.788093, 1.2}}, 
  PlotStyle -> Red, AxesLabel -> {t, k}];
plot2 = ListLinePlot[{{tthres, 10}, {tthres, 0}}, PlotStyle -> Dotted,
   AxesLabel -> {t, k}];
plot3 = ListLinePlot[{{0.00025, 0.001}, {0.170589, 1}, {0.261065, 
    2}, {0.317783, 3}, {0.35709, 4}, {0.386195, 5}, {0.408763, 
    6}, {0.426861, 7}, {0.44175, 8}, {0.454247, 9}, {0.464908, 
    10}, {0.482179, 12}, {0.495613, 14}, {0.511024, 17}, {0.522663, 
    20}, {0.536849, 25}, {0.546988, 30}, {0.55461, 35}, {0.560556, 
    40}, {0.565329, 45}, {0.569245, 50}}, PlotStyle -> Black, 
  AxesLabel -> {t, \[Theta]}]

The three plots above have different $x$ and $y$-axis. I'd like to combine them as one plot, with $\theta$ being the left $y$-axis, $k$ being the right $y$-axis, and $t\in(0,0.8)$ being the $x$-axis. Can anyone give me some hint or help? Thanks in advance!

Answer 1

1. With data1 and data3 the input lists in plot1 and plot3 in OP, find the MinMax of vertical coordinates:

yminmax1 = MinMax @ data1[[All, 2]];
yminmax3 = MinMax @ data3[[All, 2]];

2. Rescale data3 so that it has the same vertical range as data1:

data3rescaled = Transpose[{#, Rescale[#2, yminmax3, yminmax1]} & @@ 
  Transpose[data3]];

3. Plot data1 and data3rescaled together using ListLinePlot. Use tthres as GridLines, and use Charting`FindTicks to get the ticks on the left frame to match the values in data3:

ListLinePlot[{data3rescaled, data1}, 
 GridLines -> {{tthres}, None}, 
 GridLinesStyle -> Directive[AbsoluteThickness[1], Dashed], 
 PlotStyle -> {Black, Red},
 LabelStyle -> 16, 
 ImageSize -> Large, 
 Frame -> True, 
 FrameLabel -> {{θ, k}, {t, None}}, 
 FrameTicks -> {{Charting`FindTicks[yminmax1, yminmax3],  All}, 
   {Automatic, Automatic}}]