I like the question, and note that it says "the minimum length of the hairs in the peyos area." (A different and important question would be what is included in "the peyos area".)
In terms of a minimum length, Rambam (Mishneh Torah, Avodah Zarah 12:6) writes:
וּמֻתָּר לְלַקֵּט הַפֵּאוֹת בְּמִסְפָּרַיִם לֹא נֶאֱסַר אֶלָּא
It is permitted to clip the corners with a pair of scissors, for the
prohibitive commandment applies only against destroying it with a
I understand from this that one can cut it as short as desired, as long as he does not use a razor that completely "destroys" the presence of the hair on the side of the head.
However, Shulchan Aruch (Yoreh De'ah 181:3) writes:
אינו חייב אלא בתער ויש אוסרים במספרי' כעין תער ויש לחוש לדבריה':
He is not liable unless he uses a razor (like Rambam). But there are
those (e.g. Rosh) who forbid scissors that shave like a razor; and
their words should be regarded.
This is just for pe'ot, whereas for shaving the beard, he says (Yoreh De'ah 181:10):
אינו חייב על השחתת פאת הזקן אלא בתער אבל במספרים מותר אפילו כעין תער:
One is only liable for destroying the corner of the beard by means of
a razor, however by scissors it is permitted, even if it is like a
So, from what I understand, a normal electric shaver that goes down to the skin can be used on the beard, but Shulchan Aruch says not to use it on the pe'ot. There is no minimum length for the beard or for Rambam - it can be "like a razor" in that it leaves no hair! So Rambam allows a #0 cut as long as you don't use a razor. And Shulchan Aruch says the "scissors" should not be "like a razor" i.e. they have to leave some length of hair at the side of the head. Shulchan Aruch gives no measurement, so although later authorities have tried to establish what "like a razor" means by comparison with other sugyot, it is not clear that the Shulchan Aruch would have bothered so much about it, as long as you have not cut down to the skin.
Those are my thoughts from reading the sources. I am happy to be corrected on any mistakes and would not follow this piece as practice ab initio. Hope that helps.