Investigation of a universal behavior between Néel temperature and staggered magnetization density for a three-dimensional quantum antiferromagnet
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 TN/√c3 ∝ ℳs near the quantum critical point (QCP) associated with dimerization. Here TN, c, and ℳs are the Néel temperature, the spinwave velocity, and the staggered magnetization density, respectively. For all the physical quantities considered here, such as TN and ℳs, 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 TN/√c3 ∝ ℳs near the investigated QCP only sets in significantly in the region with strong spatial anisotropy.