Investigation of a universal behavior between Néel temperature and staggered magnetization density for a three-dimensional quantum antiferromagnet

Abstract

We simulate the three-dimensional quantum Heisenberg model with a spatially anisotropic ladder pattern using the first principles Monte Carlo method. Our motivation is to investigate quantitatively the newly established universal relation $T_N/\sqrt{c^3}$ $\propto$ ${\mathcal{M}}_s$ near the quantum critical point (QCP) associated with dimerization. Here $T_N$, $c$, and ${\mathcal{M}}_s$ are the Néel temperature, the spinwave velocity, and the staggered magnetization density, respectively. For all the physical quantities considered here, such as $T_N$ and ${\mathcal{M}}_s$, our Monte Carlo results agree nicely with the corresponding results determined by the series expansion method. In addition, we find it is likely that the effect of a logarithmic correction, which should be present in (3+1)-dimensions, to the relation $T_N/\sqrt{c^3}$ $\propto$ ${\mathcal{M}}_s$ near the investigated QCP only sets in significantly in the region with strong spatial anisotropy.

5 pages, 7 figures, 2 tables

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Cited by in corpus (6)

• Multiplicative logarithmic corrections to quantum criticality in three-dimensional dimerized antiferromagnets
• Excitation Gap Scaling near Quantum Critical Three-Dimensional Antiferromagnets
• Universal scalings of Néel temperature, staggered magnetization density, and spinwave velocity of three-dimensional disordered and clean quantum antiferromagnets
• Classification for the universal scaling of Néel temperature and staggered magnetization density of three-dimensional dimerized spin-1/2 antiferromagnets
• Universal scaling of three-dimensional dimerized quantum antiferromagnets on bipartite lattices
• Monte Carlo determination of the low-energy constants for a two-dimensional spin-1 Heisenberg model with spatial anisotropy