Spikes in quantum Regge calculus

For most measures in two-dimensional quantum Regge calculus proposed in the literature we show that the average values of link lengths l, [l(n)], do not exist for sufficiently high powers of n. In particular, this is also true for the nonlocal DeWitt-like measure introduced by Regge and Lund. Thus the concept of length has no natural definition in this formalism and a generic manifold degenerates into spikes. This might explain the failure of quantum Regge calculus to reproduce the continuum results of two-dimensional quantum gravity. It points to severe problems for the Regge approach in higher dimensions.