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Using examples of the square- and triangular-lattice Heisenberg models wedemonstrate that the density matrix renormalization group method (DMRG) can beeffectively used to study magnetic ordering in two-dimensional lattice spinmodels. We show that local quantities in DMRG calculations, such as the on-sitemagnetization M, should be extrapolated with the truncation error, not with itssquare root, as previously assumed. We also introduce convenient sequences ofclusters, using cylindrical boundary conditions and pinning magnetic fields,which provide for rapidly converging finite-size scaling. This scaling behavioron our clusters is clarified using finite-size analysis of the effectivesigma-model and finite-size spin-wave theory. The resulting greatly improvedextrapolations allow us to determine the thermodynamic limit of M for thesquare lattice with an error comparable to quantum Monte Carlo. For thetriangular lattice, we verify the existence of three-sublattice magnetic order,and estimate the order parameter to be M = 0.205(15).

Neel order in square and triangular lattice Heisenberg models