What do you do when the heart won't give up?

My girlfriend is an addict who isn't ready to give up, so we just split up recently. I know the path she is taking is of self destruction in more ways than one, and that for my own sanity I should let her go to live her own life, but my heart still wants to chase after her and try and bring her back and save her.
No matter how hard I try and concentrate on the hurt and pain she's caused me with her addiction over the past 3 months, I still love her, and my heart pines for her.
How do I get over this?