| Numerical studies of the 2D frustrated antiferromagnets are hindered by the absence of reliable large-scale quantum Monte Carlo methods and by large finite-size effects in other methods. Using the effective σ-model we demonstrate that the most significant finite-size effects can be eliminated by an appropriate choice of the cluster aspect ratio, allowing for much more precise estimates of observables already in small systems. Combining the improved DMRG accuracy with the use of non-traditional clusters and boundary conditions for rapidly converging finite-size scaling, we study the ordering in the square- and triangular-lattice Heisenberg models. We demonstrate the vanishing of the leading finite-size effect ~ O(1/L) in the order parameter for the sequence of clusters with the ``magic'' aspect ratio (Lx/Ly close to 2), in agreement with the effective σ-model and finite-size spin-wave theory. For the triangular lattice, we verify the existence of three-sublattice magnetic order, and estimate the order parameter to be M = 0.205(15). |
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