Recently found out that my exgirlfriend is spreading some rather nasty slander about me, what can I do?

Apparently you work in a large store. My advice is to see your boss and discuss the matter with him and ask for advice. Don't tell him a long tearful story but lay it on the line in a truthful manner. Tell him that it is hurting your reputation and you would like to have the matter concluded amicably. You do not wish to bring up personal matters in a business environment but this is getting out of hand....and you need his advice.