  Recently I proposed a simple dynamical network model for discrete space-time
which self-organizes as a graph with Hausdorff dimension d_H=4. The model has a
geometric quantum phase transition with disorder parameter (d_H-d_s) where d_s
is the spectral dimension of the dynamical graph. Self-organization in this
network model is based on a competition between a ferromagnetic Ising model for
vertices and an antiferromagnetic Ising model for edges. In this paper I solve
a toy version of this model defined on a bipartite graph in the mean field
approximation. I show that the geometric phase transition corresponds exactly
to the antiferromagnetic transition for edges, the dimensional disorder
parameter of the former being mapped to the staggered magnetization order
parameter of the latter. The model has a critical point with long-range
correlations between edges, where a continuum random geometry can be defined,
exactly as in Kazakov's famed 2D random lattice Ising model but now in any
number of dimensions.
