I read in a forum that 12px english/roman character will appear to be readable while a 12px japanese character would be very heard to read. This brings me to the question, "Is there an ideal font size that one can use in their application, especially when their application supports more than one language?"
Actually, after writing that comment, I think I've thought of an answer the question.
No, I don't think there is an ideal multilingual font size. The question is akin to asking "what is the ideal font size to use in the user interface for software that does everything for everyone?". It depends on context, purpose, audience and all the other usual factors that go into a decision like this.
Furthermore, we already know that different scripts have very different levels of visual density - that's the whole point of this question - but it then follows that it must be impossible for a single absolute font size to be maximally legible across all types of script. A variable font size option may be the best solution to this problem.
Note that people are typically able to read text in scripts they're familiar with without major problems across a wide range of sizes, as reading is a complex process that isn't just pure visual processing -- and if users have problems with reading small text in general, that's a different accessibility issue altogether.
On a related note, here is my earlier comment, slightly edited:
Keep in mind that although a 12px kanji character may appear to be very hard to read, people used to logographic scripts regularly read tiny print in newspapers with no problem. Like with alphabetic scripts, there is a process of statistical inference going on; we recognize common words by general shape and context in addition to the components of the character. I don't know how to answer the question of "ideal" font size, but for practical reasons East Asian localizations often use the same sizes as the Latin script counterparts with no (AFAIK anecdotally) major usability problems.
The ideal font size, for any typeface is 1em.
That is the size the glyphs were intended to be displayed at, the size they are designed to be displayed at.
Why second-guess the typographer who created the typeface, the OS / Browser manufacturer or your users (who may set their own preferred default font-size on the device)?
Do nothing at all and all your type will render at the size it was designed to, on every device, in every language, all of the time. If you set the default font-size of your app in px you completely disregard the choices made by the type designer, the device / OS developers and your users; all of whom had good reasons for the choices they made.