We study supersymmetric Yang-Mills theories on the three-sphere, with massive matter and Fayet-Iliopoulos parameter, showing second order phase transitions for the non-Abelian theory, extending a previous result for the Abelian theory. We study both partition functions and Wilson loops and also discuss the case of different R-charges. Two interpretations of the partition function as eigenfunctions of the A1 and free AN−1 hyperbolic Calogero-Moser integrable model are given as well.