Using Greek $\LaTeX$ fonts

I can no longer get this working. The commands shown below don't give me an output with the correct typeface with Greek letters. I don't know why.

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tl;dr Use the Latin Modern Math OpenType fonts downloadable from here and make all Greek italic.

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According to my research this is not a Mathematica-specific issue. The Computer Modern fonts do not have a full set of Greek letters and were not meant to typeset Greek. This means that even the Unicode OpenType-packaged Latin Modern set of fonts doesn't include Greek glyphs. The CM fonts only have those Greek glyphs that are needed for typesetting math and look different from their Latin counterpart. E.g. α is included but not Α (capital alpha).

The Latin Modern Roman set of fonts is meant for typesetting text and has no Greek.

The Latin Modern Math set of fonts is meant for typesetting math, and has Greek, but it's not suitable for typesetting text. It is very likely sufficient for figure labels though.

If you install Latin Modern Math, and then restart Mathematica, you will be able to use Greek letters. The catch is that they only look good when explicitly made italic. You'll need to format all Greek as italic manually and the rest of the text as upright.

Here's a demonstration and a comparison with $\LaTeX$ to show that it's indeed the same font:

Unfortunately I do not know how to get the variants working:

I think the Latin Modern Math is the same font as cmmi10 but it's packaged differently (following this standard?) to make it compatible with modern math typesetting software like recent versions of MS Word.

What you could do is download and install the STIX fonts by following the instructions here. These fonts are (if I'm not mistaken) also used by MathJAX, the engine that renders $\LaTeX$ code on this web site.

Then, in Mathematica, do something like this:

baseStyle = {FontFamily -> "STIXGeneral", 12, 
          ScriptSizeMultipliers -> .66, ScriptMinSize -> 6};

    Map[SetOptions[#, BaseStyle -> baseStyle] &, {Plot, ListPlot}];

    Plot[Sin[x], {x, -2, 2}, 
      AxesLabel -> {HoldForm@Subscript[x, 1], 
          HoldForm@Sin[Subscript[x, 1]]}]

The STIX fonts could also be replaced by "Times New Roman", but I suggest the former because they are designed for scientific typesetting and have all the necessary symbols, including Greek. In the Map command, I apply this choice of fonts to the types of plots I think are needed. You can customize the list {Plot, ListPlot} to whatever you like.

Even though this question was asked quite some time ago, the problem is still relevant today I believe (at least for me it was).

I found that combining yohbs' approach using "FromCharacterCode" and the OpenType-Font "Latin Modern Math" works very well for me (I now use this workflow on Mathematica 12.0).

The character codes for the corresponding Greek letters can be looked up in LibreOffice:

I hope this was of help to someone!