  Spin Foam Models (SFMs) are covariant formulations of Loop Quantum Gravity
(LQG) in 4 dimensions. This work studies the perturbations of SFMs on a flat
background. It demonstrates for the first time that smooth curved spacetime
geometries satisfying Einstein equation can emerge from discrete SFMs under an
appropriate low energy limit, which corresponds to a semiclassical continuum
limit of SFMs. In particular, we show that the low energy excitations of SFMs
on a flat background give all smooth solutions of linearized Einstein equations
(spin-2 gravitons). This indicates that at the linearized level, classical
Einstein gravity is indeed the low energy effective theory from SFMs. Thus our
result heightens the confidence that covariant LQG is a consistent theory of
quantum gravity. As a key technical tool, a regularization/deformation of the
SFM is employed in the derivation. The deformation parameter $\delta$ becomes a
coupling constant of a higher curvature correction term to Einstein gravity
from SFM.
