When people fall in love, and then fall back out of it, sometimes the former partner gets on the rag. Infidelity occurs when people don't understand that human beings can get horny for other people and lose interest in you.
When this happens and you're not married, you may lose a sofa, your car, or even the apartment lease. In that case, give it up. It ain't worth it.
When you are married, it can lead to, for example, indigestion, migraines, lawsuits, and/or murder. Do not assume that you can remain friends. That misapprehension can be removed with a vigorous application of vinegar to all remaining souvenirs: do not make the mistake of keeping, for instance, old pillowcases because they smell like the beloved.
Courses of Action
Break completely with the past. It is best to kill both your former lover and his/her new paramour, assuming, of course, that you can do so without incurring the interest of the police. If the police do themselves become involved, move, grow a beard (you too, ladies), and answer any question about your ex with the phrase, "Yeah I've turned some tricks in my day but I'd never stoop THAT low." This should get you far enough away in both time and distance for you to start the process again with another unfortunate individual.
Otherwise, do not continue to stalk your former lover, unless you think you can get some money out of it. Or maybe if you want to freak the shit out of them. Then it's all good too. Just do it properly.