A novel scenario for the emergence of geometry in random multitrace matrix
models of a single hermitian matrix $M$ with unitary $U(N) $ invariance, i.e.
without a kinetic term, is presented. In particular, the dimension of the
emergent geometry is determined from the critical exponents of the
disorder-to-uniform-ordered transition whereas the metric is determined from
the Wigner semicircle law behavior of the eigenvalues distribution of the
matrix $M$. If the uniform ordered phase is not sustained in the phase diagram
then there is no emergent geometry in the multitrace matrix model.Comment: 18 pages, 7 figures (16 graphs), 1 tabl