(a)-(b): Comparison of Langevin results with Monte Carlo. (a) The ferromagnetic feature Ss(0, 0) in the magnetic structure factor and (b) the Fourier transform of the density-density correlation Sn at q = (π, π). There is a very good agreement for the chosen Ds and D ph values. (c) The dependence of Ss(0, 0) on Ds for three values Ds = 0.025, 0.05, 0.1, and (d) of Sn(π, π) on D ph for three values D ph = 0.1t, 0.5t, 1.0t. In both cases, we see an insensitivity to dissipation rates.