Q.Can someone help me identify these weeds?
I live in Phoenix, Arizona and noticed a something growing on the other side of my cement wall. When I went over to look, it was a HUGE cluster of weeds. My husband chopped them all down with a weed wacker but I’m pretty sure they are going to grow back. I want to keep them from growing into my yard under the wall. Can anyone recognize any of these weeds and give me a suggestion on getting rid of them permanently? I have Ficus Nitida on my side of the wall I don’t want to hard.

Thistle, mallow and maybe another I'm not sure about.
It is doubtful that they will grow under the footing of a block wall. It's more likely that they will spread by wind blown seed. Keep an eye on your side of the wall for young weed growth, and dig or pull before they mature and go to seed in your yard.
If you have property owner permission on the other side where your husband cut, and you are competent with safe and effective use of pesticides, then you can use an "organic" or chemical herbicide (weed killer), general purpose or selective for "broadleaf" weeds.
http://www.saferbrand.com/safer-brand-fast-acting-weed-and-grass-killer-rtu-32-oz-5055-6