  Two-dimensional quantum gravity, defined either via scaling limits of random
discrete surfaces or via Liouville quantum gravity, is known to possess a
geometry that is genuinely fractal with a Hausdorff dimension equal to 4.
Coupling gravity to a statistical system at criticality changes the fractal
properties of the geometry in a way that depends on the central charge of the
critical system. Establishing the dependence of the Hausdorff dimension on this
central charge $c$ has been an important open problem in physics and
mathematics in the past decades. All simulation data produced thus far has
supported a formula put forward by Watabiki in the nineties. However, recent
rigorous bounds on the Hausdorff dimension in Liouville quantum gravity show
that Watabiki's formula cannot be correct when $c$ approaches $-\infty$. Based
on simulations of discrete surfaces encoded by random planar maps and a
numerical implementation of Liouville quantum gravity, we obtain new
finite-size scaling estimates of the Hausdorff dimension that are in clear
contradiction with Watabiki's formula for all simulated values of $c\in
(-\infty,0)$. Instead, the most reliable data in the range $c\in [-12.5, 0)$ is
in very good agreement with an alternative formula that was recently suggested
by Ding and Gwynne. The estimates for $c\in(-\infty,-12.5)$ display a negative
deviation from the latter formula, but the scaling is seen to be less accurate
in this regime.
