Antiferromagnetism beyond the classical percolation threshold in the diluted half-filled one-band Hubbard model in three dimensions

We investigate the impact of dilution by setting the on-site repulsion strength U to zero at a fraction of sites in the half filled Hubbard model on a simple cubic lattice. We employ a semiclassical Monte Carlo approach first to recover the zero dilution (undiluted x = 1) properties, including U dependence of insulator to metal crossover temperature scale T* and long-range staggered antiferromagnetic ordering temperature T-N. For the nonperturbative regime of U approximate to bandwidth, we find a rapid suppression of T* with reducing x from 1 to 0.7. However, TN remains unchanged in this dilution range, showing a weakening of the insulating state but not of the magnetic order. At x <= 0.7, T* and T-N coincide and are suppressed together with decrease in x. Within the Monte Carlo study we show that the long-range magnetic order vanishes at x = 0.15 at T = 0.01 much below the classical percolation threshold. The magnetic order below the classical percolation threshold is in line with the expected fragile long-range magnetic order at vanishingly small x at T = 0. We exhibit that the induced moments on U = 0 sites drive the magnetic order below the classical percolation limit by studying local moment systematics and finite-size analysis of magnetic order. At the end, we show that either increasing U to large values or raising temperature beyond a U dependent critical value, suppresses the induced local moments of the U = 0 sites and recovers the classical percolation threshold.