Apply PhD with no recommendation Please allow me to ask for suggestion about no recommendation problem. 
I graduated my master with distinction and my paper was published in nation wide journal, everything seems to be perfect. But after the graduation,  my thesis supervisor has a personal problem with me and we've never talked since then. So now I want to apply for PhD and when it comes to recommendation, I really don't know what to do and I don't think my supervisor will write a good thing about me since we are in personal conflict. 

Do you have any suggestion for this situation?
If you can be open with your formal supervisor about the "personal problem" s/he has with you, you could simply ask, "I am interested in pursuing a PhD. I know that we have disagreed about XYZ and so I wanted to ask you if you believe you could write me a fair recommendation."

Note, that this is still risky - the supervisor can write a bland recommendation (which holds little weight) or agree to write it and write a bad one anyway. 

What about the director of the program you attended? That could be weighed more favorably. Other faculty members? My PhD dissertation chair never wrote recommendations for anyone, so I never even asked him (we never had a falling out or anything, it was just his personal policy). It never hurt my chances of jobs or other things because I had other faculty and references write litters for me instead. 

Good luck!