  Phase transitions with spontaneous symmetry breaking are expected for group
field theories as a basic feature of the geometogenesis scenario. The following
paper aims to investigate the equilibrium phase for group field theory by using
the ergodic hypothesis on which the Gibbs-Boltzmann distributions must break
down. The breaking of the ergodicity can be considered dynamically, by
introducing a fictitious time inducing a stochastic process described through a
Langevin equation, from which the randomness of the tensor field will be a
consequence. This type of equation is considered particularly for complex
just-renormalizable Abelian model of rank d = 5, and we study some of their
properties by using a renormalization group considering a coarse- graining both
in time and space.
