  We study the large N saddle points of weakly coupled N=4 super Yang-Mills
theory on S^1 x S^3 that are described by a commuting matrix model for the
seven scalar fields {A_0, \Phi_J}. We show that at temperatures below the
Hagedorn/`deconfinement' transition the joint eigenvalue distribution is S^1 x
S^5. At high temperatures T >> 1/R_{S^3}, the eigenvalues form an ellipsoid
with topology S^6. We show how the deconfinement transition realises the
topology change S^1 x S^5 --> S^6. Furthermore, we find compelling evidence
that when the temperature is increased to T = 1/(\sqrt\lambda R_{S^3}) the
saddle with S^6 topology changes continuously to one with S^5 topology in a new
second order quantum phase transition occurring in these saddles.
