Emergence of gravity from interacting simplices

We consider a statistical model of interacting 4-simplices fluctuating in an N-dimensional target space. We argue that a gravitational theory may arise as a low energy effective theory in a strongly interacting phase where the simplices form clusters with an emergent space and time with the Euclidean signature. In the large N limit, two possible phases are discussed, that is, `gravitational Coulomb phase' and `gravitational Higgs phase'.