512MB is borderline able to run android 4.1, (you get about 100-150MB of RAM free to run your apps.
most apps run fine with that except the web browser which freezes if you try sites like 4chan or similar sites where a single thread can have 100+ images, the browser will just eat all available memory and then force quit.
(some browsers like chrome will unload non visible areas to deal with limited memory but it slows the overall experience and scrolling, and .gif heavy sites will still crash it.
for android 3.x and up, 1GB is the minimum amount of RAM, accept no less.