Go look at your plant and see if there are aphids under the leaves. If so then the soap and water trick might work because it's the aphid's waste that the ants are really after. And, soapy water takes out aphids whose only purpose on this Earth is to annoy gardeners.

Usually just a good spray from the hose will knock them off though. Too much soapy water will hurt plant leaves. When I use it, I rinse the plant off within 15 or so minutes.

But, if the ants are really eating your plant--and here in the desert some do that--you've got to get rid of them. Find their mound or ant hole and kill them. One method I've used successfully is to pour boiling water down their hole. Pour slowly. I usually have to make several pours of 1 pint of water each. Obviously, if your ant hill is right next to a tomato plant, you've got to do something else. You don't want to cook your plant roots.

You can add a little dish soap to this water because it does stick to the ants and block their ability to breath.
And, the water doesn't have to be actually boiling, it just has to be hot enough to kill those ants.

I've used this on fire ants, harvester ants and others.

If the ants are outside my veggie and herb garden, I'll go ahead and use Amdro.

For those little eenie weenie ants, try Terro Bait. That's safe stuff. It's basically boric acid and sugar syrup. I've used that indoors.

There's a lot of info on the web about controlling ants.
A lot of it just doesn't work here. I know you've read about ants being repelled by mint. Maybe some ants are repelled by mint. I've had ants in my mint bed.

Good luck.

Thanks for the advice.. The soapy water spray didn't seem to help much... So I've been using just plain water spray from the hose to keep knocking the ants off the eggplant leaves... In the morning I'll look to see if there are aphids the ants are after... But as best I could see today, the ants themselves are eating away at the plant, the stems to several of the new leaves have been chewed off... Might be time for more desperate measures...

Leaf cutting ants aren't common in Arizona, but still possible. You might want to spend time with a lawn chair and a cold drink, ant watching: leaf cutting ants will be carrying pieces of leaves back to the nest--sometimes looking like little surf-sailors!
More likely, caterpillars or grasshoppers are eating the leaves, and the ants are (more or less) innocent bystanders.
Organic remedies for ants: diatomaceous earth, or ground-up orange peel.
For caterpillars: Dipel dust, B. t. spray, or spinosad.
For grasshoppers: spinosad, or neem oil.
Good luck!

ant remedies
Spinosad
Amdro
I have the same ant problem. I like growing egg plant and Green peppers. The first year I tried it , it was very good. I used goat dung for fertilizer. No ants! But this year I have an invasion of those little brown ants and the eat the little flower buds of my green peppers. I tried that white power that is suppose to get rid of them, but that didn't work. Later I made a concoction of cayenne pepper, ginger power,cinnamon, garlic power and lemon skins. It seems to stave them off long enough for the peppers to grow but they still keep coming back. I especially put some at the root of the plants because they build their nests there.

meeksam, we haven't seen a single ant eat any of our blossoming veggies, they do swarm about the flowers and plants and aerate the soils, however they have carried off a few seeds and some spoiled/bad fruit. Other than that I would leave them alone, as they are a sign of a healthy garden, and do signal that you may have other problems ie APHIDS or caterpillars. Plus it gives birds, lizards and other predators something to eat.

meeksam, I have to retract a portion of my response.

I am watching some very nasty and aggressive black ants just munching away on our okra buds. They've munched huge holes in the fruit, carrying off bits back to their home :(