  Regarding metric fluctuations as generating {\it roughness} on the fabric of
the otherwise smooth vacuum, it is shown that in its simplest form, the effect
can be described by the scalar $\phi^4$ model. The model exhibits a second
order phase transition between a smooth (low-temperature) phase and a rough
(high-temperature) one, corroborating the absence of metric fluctuations at low
energies. In the rough phase near the critical point, vacuum is characterized
by a power-law behavior for the fluctuating field with critical exponent $\beta
\approx 0.33$.
