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The definition of a double-scaling limit represents an important goal in thedevelopment of tensor models. We take the first steps towards this goal byextracting and analysing the next-to-leading order contributions, in the 1/Nexpansion, for the IID tensor models. We show that the radius of convergence ofthe NLO series coincides with that of the leading order melonic sector.Meanwhile, the value of the susceptibility exponent at NLO is 3/2, signaling adeparture from the leading order behaviour. Both pieces of information provideclues for a non-trivial double-scaling limit, for which we put forward someprecise conjecture.

Towards a double-scaling limit for tensor models: probing sub-dominant orders