It is actually two separate pieces the light part is just a post lamp. There are many very similar square lights like that to choose from. They attach by the separate base mount such as these.

http://www.1800lighting.com/Outdoor-Lighting-Mounting-Hardware-Outdoor-Pier-Mount-Adapter/mn/N-ad

Thanks, Fred. It's great to identify a base that's similar. I have been looking though the post lamps but can't seem to find one that has the open support design at the bottom, so that's why I'm trying to figure out which specific lanterns they are. I'll keep looking! Thx again!

the fact that it has a small brass plate on it, might help. not many do that. either of these could work , they have whats called pier mount with the base built in. it bothers me that they dont match in the photo lol. tho you can get matching ones, these are ideas. give hinkley a try.
http://www.amazon.com/Hinkley-Lighting-Trellis-Collection-Regency/dp/B00BF2YIE6

http://www.hinkleylighting.com/product/Greystone-Bingham-Lanterns-12

http://www.hinkleylighting.com/product/Oil-Rubbed-Bronze-Lincoln-Lanterns-2 is this it? it can go on a plaster btw.