  Motivated by recent experimental observations [Phys. Rev. 96, 020407 (2017)]
on hexagonal ferrites, we revisit the phase diagrams of diluted magnets close
to the lattice percolation threshold. We perform large-scale Monte Carlo
simulations of XY and Heisenberg models on both simple cubic lattices and
lattices representing the crystal structure of the hexagonal ferrites. Close to
the percolation threshold $p_c$, we find that the magnetic ordering temperature
$T_c$ depends on the dilution $p$ via the power law $T_c \sim |p-p_c|^\phi$
with exponent $\phi=1.09$, in agreement with classical percolation theory.
However, this asymptotic critical region is very narrow, $|p-p_c| \lesssim
0.04$. Outside of it, the shape of the phase boundary is well described, over a
wide range of dilutions, by a nonuniversal power law with an exponent somewhat
below unity. Nonetheless, the percolation scenario does not reproduce the
experimentally observed relation $T_c \sim (x_c -x)^{2/3}$ in
PbFe$_{12-x}$Ga$_x$O$_{19}$. We discuss the generality of our findings as well
as implications for the physics of diluted hexagonal ferrites.
