I tried a bunch of things; the number #1 liquid ant borox bait trap killer gizmo on Amazon just made a bunch of them die, but it didn't kill the colony. I just kept laying out more and more traps, but the ants would just die and fill up the trap, then the other ants would somehow learn that the trap was bad, and never touch it again, but interestingly enough, they would go in, and carry away their dead comrades.
Apparently, because Argentine ants have multiple queens, forming a giant macro colony that vertically spans the entire state of California. You get one queen, and they won't be down for the count, they'll just come right back. These are stubborn, resilient little buggers.
I then tried caulking the cracks along the bottom of the sheetrock next to my windows that they would keep coming out of, and I sealed that whole thing up good; it worked for about a week, and then the ants managed to eat through the caulking!
Anyhow, there were aphids were all over the vines(?) going all the way up the side of my house and up over my window. Once we removed the vines entirely, the ants were gone for good.
Sorry about the incomplete sentences and run-ons, I'm tired...