  We study a three matrix model with global SO(3) symmetry containing at most
quartic powers of the matrices. We find an exotic line of discontinuous
transitions with a jump in the entropy, characteristic of a 1st order
transition, yet with divergent critical fluctuations and a divergent specific
heat with critical exponent $\alpha=1/2$. The low temperature phase is a
geometrical one with gauge fields fluctuating on a round sphere. As the
temperature increased the sphere evaporates in a transition to a pure matrix
phase with no background geometrical structure. Both the geometry and gauge
fields are determined dynamically. It is not difficult to invent higher
dimensional models with essentially similar phenomenology. The model presents
an appealing picture of a geometrical phase emerging as the system cools and
suggests a scenario for the emergence of geometry in the early universe.
