Quite a few different ways to skin the cat..
Some diagonal wood braces let into the wall running at 45° from the bottom to top of wall,or if the inside is remaining unfinished attached to the inside(probably like it is now?) , sometimes a metal strap is used for the same purpose, sometimes installing 1 piece of plywood on each will suffice.
Either way it's not likely to fall down I see places being built like this often..lol.. Purlins and board and batton alone aren't technically enough to resist the wall from moving though.