Just about any major distribution should be about the same. What you want to look at instead of 'What distribution should I use for 512M?', the real question is: 'What desktop environment should I use with 512M?'
I would suggest staying away from any environment which uses Compiz or a fancy graphical desktop of any sort. From what I saw of your laptop specifications, you should avoid Unity desktop, KDE, or standard GNOME 3.x. Xfce is available in Linux Mint 13, or MATE installation, or you can install one of those and later install LXDE in place of the default desktop. OpenBox is not directly supported in Mint, but you can install that desktop as well and have a fairly responsive machine.
Full-fat applications like LibreOffice/OpenOffice, Firefox, Thunderbird, Evolution, GIMP, and Banshee may also stress your computer and make it crawl, especially with multiple applications open.
You don't have to go all the way down to AntiX, Puppy, Slitaz, DamnSmallLinux, or Tiny Core Linux, just match your expectations to your hardware. To use an analogy from the Evil Empire, don't expect to run Vista on a 256M XP installation.
LMDE Mate 64-bit, LM17.3 Cinnamon 64-bit
Debian Mate 64-bit, Xubuntu xenial 64-bit, Ubuntu-Mate 14.04 64-bit, Antergos Xfce 64-bit, PCLinuxOS Mate 64-bit