Phase boundary near a magnetic percolation transition

Motivated by recent experimental observations [Rowley et al. in 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 $$p_\mathrm{c}$$ p c , we find that the magnetic ordering temperature $$T_\mathrm{c}$$ T c depends on the dilution p via the power law $$T_\mathrm{c} \sim |p-p_\mathrm{c}|^\phi $$ T c ∼ | p - p c | ϕ with exponent $$\phi =1.09$$ ϕ = 1.09 , in agreement with classical percolation theory. However, this asymptotic critical region is very narrow, $$|p-p_\mathrm{c}| \lesssim 0.04$$ | p - p c | ≲ 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 $$T_\mathrm{c} \sim (x_\mathrm{c} -x)^{2/3}$$ T c ∼ ( x c - x ) 2 / 3 in PbFe $$_{12-x}$$ 12 - x Ga $$_x$$ x O $$_{19}$$ 19 . We discuss the generality of our findings as well as implications for the physics of diluted hexagonal ferrites. Graphic abstract