That will run Minecraft. One thing to note, is you need 64bit Java to really amp up the amount of memory you can use. So that means 64 bit OS. Otherwise, you can easily run out of memory around lava and water regardless if you're running it on a toaster, or with SLI GTX680's.
So, 64bit OS, and at least 8G of ram so the OS doesn't run out of memory. That game is more of a memory hog than anything else.