Do professors from different universities (but in the same field) contact each other about the students who applied to their programs?
People might discuss the pool of applicants generally—what percent is international, what was the admit rate, etc.—but never an individual candidate's application. 

The only time I could imagine an admission committee member discussing a candidate's application is if someone on the committee (or in the department, if it's more decentralized) knows one of the people who wrote the candidate's letters of reference and wants to get more direct information than what's written in the letter.