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If I have a list data (http://pastebin.com/RgWLJmTS) which is about to be plotted with

ListLogPlot[{data}, Frame -> True, Joined -> True, 
PlotStyle -> {Red, Thickness[0.001]}],

But I need to have a plot with a thin line of Joined plotted data. With above commend I can not manage the thickness of the Joined line!

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You incorrectly use the PlotStyle syntax, please read the second statement under the "Details" section:

PlotStyle->{g1,g2,...} specifies that successive directives gi should be used cyclically for successive objects.

For avoiding ambiguity it is recommended to wrap your style directives (which should be applied to individual dataset) with Directive:

ListLogPlot[{data}, Frame -> True, Joined -> True, 
 PlotStyle -> {Directive[Red, Thickness[0.001]]}]

plot

Another alternative is to add additional curly brackets:

ListLogPlot[{data}, Frame -> True, Joined -> True, PlotStyle -> {{Red, Thickness[0.001]}}]

plot

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