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Colored tensor models have been recently shown to admit a large N expansion,whose leading order encodes a sum over a class of colored triangulations of theD-sphere. The present paper investigates in details this leading order. We showthat the relevant triangulations proliferate like a species of colored trees.The leading order is therefore summable and exhibits a critical behavior,independent of the dimension. A continuum limit is reached by tuning thecoupling constant to its critical value while inserting an infinite number ofpairs of D-simplices glued together in a specific way. We argue that thedominant triangulations are branched polymers.

Critical behavior of colored tensor models in the large N limit