Scaling of the leg ( c ) and rung ( d ) currents as a function of K / J (averaged over 140 plaquettes and 200 snapshots per point). The solid line is a fit of an ED simulation of the ideal currents, with the amplitude as a single free parameter, yielding 0.78(4) for the legs and 0.71(4) for the rungs; the shaded area denotes the 1 σ confidence interval of the fit. The dashed lines indicate the currents in a non-interacting plaquette with the same fit amplitude. The error bars denote the standard error of the mean (s.e.m.), and if not visible, are smaller than the marker size. All the numerical simulations take into account the reduced flux in isolated plaquettes of 0.71(2) x π/2 (Supplementary Section II-E ).
