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Abstract: The partition function of general N = 2 supersymmetric SU(2) Yang-Mills theories on a four-sphere localizes to a matrix integral. We show that in the decompactification limit, and in a certain regime, the integral is dominated by a saddle point. When this takes effect, the free energy is exactly given in terms of the prepotential, F = −R2Re(4piiF), evaluated at the singularity of the Seiberg-Witten curve where the dual magnetic variable aD vanishes. We also show that the superconformal fixed point of massive supersymmetric QCD with gauge group SU(2) is associated with the existence of a quantum phase transition. Finally, we discuss the case of N = 2 ∗ SU(2) Yang-Mills theory and show that the theory does not exhibit phase transitions. ar X i