can I upgrade the CPU to Ivy Bridge

Ok, I have a i5 Mac Mini 2011 which uses Intel's HD graphics. It's RAM has been upgraded to 8GB. And frankly, games still run like molasses on it, especially when output to my 1080p display.

I understand from Intel that Ivy Bridge CPUs are completely backwards compatible electrically with Sandy Bridge CPUs. I'd like to exchange the chip on the Mac Mini for an Ivy Bridge one. Is it possible? I initially bought it just to sync my iPad and to learn to program for Mac OS X and iOS, but now I'd like to use it for a little bit of gaming as well. Problem is, Portal 2 and Team Fortress 2 is barely playable at 1080p (everything tuned down to medium) despite Intel's claim, and Duke Nukem Forever and Starcraft 2 can't runs like a slideshow at 1080p with everything in minimum. According to Intel, Ivy Bridge machines will come with even better integrated GPUs which can really handle HD gaming properly this time around, which is why I want to upgrade. But I cannot afford a new Mac at the moment, and am not even done paying off the 12-month installment on the existing Mac Mini (plus, I don't want to lose another activation from my Bejeweled 2 license- because this is certain to happen if I get a new Mac).

So, it comes down to this. Can it be done?