The low-energy constants, namely the spin stiffness ρs, the staggered magnetization density ℳs per area, and the spinwave velocity c of the two-dimensional (2D) spin-1 Heisenberg model on the square and rectangular lattices are determined using the first principles Monte Carlo method. In particular, the studied models have different antiferromagnetic couplings J1 and J2 in the spatial 1- and 2-directions, respectively. For each considered J2∕J1, the aspect ratio of the corresponding linear box sizes L2∕L1 used in the simulations is adjusted so that the squares of the two spatial winding numbers take the same values. In addition, the relevant finite-volume and -temperature predictions from magnon chiral perturbation theory are employed in extracting the numerical values of these low-energy constants. Our results of ρs1 are in quantitative agreement with those obtained by the series expansion method over a broad range of J2∕J1. This in turn provides convincing numerical evidence for the quantitative correctness of our approach. The ℳs and c presented here for the spatially anisotropic models are new and can be used as benchmarks for future related studies.
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