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 /√c ³ ∝ ℳ _s near the quantum critical point (QCP) associated with dimerization. Here T _N , c, and 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 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 /√c ³ ∝ ℳ _s near the investigated QCP only sets in significantly in the region with strong spatial anisotropy.