Should I break up with my boyfriend if he and his ex still talk? Calling each other sexy and papi and mami?

My boyfriend and his ex still talk and from what I can see on Facebook she still calls him sexy... I can't look at his phone because he always locks it. They were in a 2 year relationship and then him and I dated and he cheated on me with her and I gave him a second chance and this sexy stuff is still going on! Should I listen to my head and break up or listen to my heart and stay in the relationship?
Should I break up with my boyfriend if he and his ex still talk? Calling each other sexy and papi and mami?
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