  Four-dimensional simplicial quantum gravity is modified either by coupling it
to U(1) gauge fields or by introducing a measure weighted by the orders of the
triangles. Strong coupling expansion and Monte Carlo simulations are used.
Although the two modifications of the standard pure-gravity model are
apparently very distinct, they produce strikingly similar results, as far as
the geometry of random manifolds is concerned. In particular, for an
appropriate choice of couplings, the branched polymer phase is replaced by a
crinkled phase, characterized by the susceptibility exponent $\gamma < 0$ and
the fractal dimension $d_H > 2$. The quasi-equivalence between the two models
is exploited to get further insight into the extended phase diagram of the
theory.
