All depends whether you can afford to pay the mortgage and rent. If you stop paying 1/2 the mortgage, you are reducing your investment in the property. Probably the best thing to do is have a chat with your mortgage provider and find out what the penalties would be - weigh up the implications of selling up, buying out or sticking it out - and then decide whats right for you.
Bear in mind that other things may be in joint names, (or maybe just your name) too, ESB, gas/oil, phone - if things are really bad between you and your partner - are they the type of person who'd run up big bills with your name on??