Ascending a "4mm" Rope with Schwabisch Hitches
 The "rope" here is blueish Marlow Excel Racing line, reported as 4mm (2200 lbs tensile strength), actual measurements closer to 4.4mm; the sheath is PET and the core is Dyneema. The green cord, used for eye-to-eye prusiks,  is nominally 4mm Spyderline (also PET sheath, Dyneema core; closer to 4.8mm).

Below is the movie of a test ascent:

Here is how the knots attached to the "main" blue line. The yellow loop is girth-hitched through the lower prusik eyes, and used for the foot loop. The upper prusik eyes go directly over a carabiner. Schwabisch hitches have many advantages over normal prusik hitches: they can be used on cords of roughly the same diameter, and the hitches can be released (moved) more easily after being weighted. They can be used on doubled ropes, unlike most mechanical ascenders.

Why would someone ever use this? Several times we have thrown a thin rope over the top of a rocky spire, attached the far side to an anchor and ascended the near side. One spire required a 3000' elevation gain over class 3 and 4 rock and snow to reach. We had to keep the gear light enough so a specially-made rope bag could be tossed over the top of the spire with at least 100' cord. In this particular trip, we ended up using a 6mm line, but the 4mm line was with us in reserve.

Have I tested the strength of this setup? Yes. I only know that pulling a single eye-to-eye prusik at 900 lbs did not damage or desheath the rope.
 
You can get by with traditional Prusik hitches on 6mm, but they are harder to move, and simply don't work with thinner rope. Note how much more difficult it is to move the hitch to the foot loop, once it is weighted.