  The sol-gel transition is studied in two purely entropic models consisting of
hard spheres in continuous three-dimensional space, with a fraction $p$ of
nearest neighbor spheres tethered by inextensible bonds. When all the tethers
are present ($p=1$) the two systems have connectivities of simple cubic and
face-centered cubic lattices. For all $p$ above the percolation threshold
$p_c$, the elasticity has a cubic symmetry characterized by two distinct shear
moduli. When $p$ approaches $p_c$, both shear moduli decay as $(p-p_c)^f$,
where $f\simeq 2$ for each type of the connectivity. This result is similar to
the behavior of the conductivity in random resistor networks, and is consistent
with many experimental studies of gel elasticity. The difference between the
shear moduli that measures the deviation from isotropy decays as $(p-p_c)^h$,
with $h\simeq 4$.
