Finite-temperature ordering of dilute graphene antiferromagnets

We employ large-scale quantum Monte Carlo simulations to study the magnetic ordering transition among dilute magnetic moments randomly localized on the graphene honeycomb lattice, induced by long-ranged Ruderman-Kittel-Kasuya-Yoshida interactions at low charge-carrier concentration. In this regime the effective exchange interactions are ferromagnetic within each sublattice, and antiferromagnetic between opposite sub-lattices, with an overall cubic decay of the interaction strength with the separation between the moments. We verify explicitly, that this commensurability leads to antiferromagnetic order among the magnetic moments below a finite transition temperature in this two-dimensional system. Furthermore, the ordering temperature shows a crossover in its power-law scaling with the moments' dilution from a low- to a high-concentration regime.