The large- $N$ expansion of the quasi-two-dimensional quantum nonlinear $\ensuremath{\sigma}$ model is used in order to establish experimentally applicable universal scaling relations for the quasi-two-dimensional Heisenberg antiferromagnet. We show that, at $N=\ensuremath{\infty}$, the renormalized coordination number introduced by Yasuda et al. [Phys. Rev. Lett. 94, 217201 (2005)] is a universal number in the limit of ${J}^{\ensuremath{'}}∕J\ensuremath{\rightarrow}0$. Moreover, similar scaling relations proposed by Hastings and Mudry [Phys. Rev. Lett. 96, 027215 (2006)] are derived at $N=\ensuremath{\infty}$ for the three-dimensional static spin susceptibility at the wave vector $(\ensuremath{\pi},\ensuremath{\pi},0)$, as well as for the instantaneous structure factor at the same wave vector. We then use $1∕N$ corrections to study the relation between interplane coupling, correlation length, and critical temperature, and show that the universal scaling relations lead to logarithmic corrections to previous mean-field results.The large-$N$ expansion of the quasi-two-dimensional quantum nonlinear $\ensuremath{\sigma}$ model is used in order to establish experimentally applicable universal scaling relations for the quasi-two-dimensional Heisenberg antiferromagnet. We show that, at $N=\ensuremath{\infty}$, the renormalized coordination number introduced by Yasuda et al. [Phys. Rev. Lett. 94, 217201 (2005)] is a universal number in the limit of ${J}^{\ensuremath{'}}∕J\ensuremath{\rightarrow}0$. Moreover, similar scaling relations proposed by Hastings and Mudry [Phys. Rev. Lett. 96, 027215 (2006)] are derived at $N=\ensuremath{\infty}$ for the three-dimensional static spin susceptibility at the wave vector $(\ensuremath{\pi},\ensuremath{\pi},0)$, as well as for the instantaneous structure factor at the same wave vector. We then use $1∕N$ corrections to study the relation between interplane coupling, correlation length, and critical temperature, and show that the universal scaling relations lead to logarithmic corrections to previous mean-field results.

arXiv:cond-mat/0606032Physical Review BNov 3, 20067 citations

The large-

N

expansion of the quasi-two-dimensional quantum nonlinear $\ensuremath{\sigma}$ model is used in order to establish experimentally applicable universal scaling relations for the quasi-two-dimensional Heisenberg antiferromagnet. We show that, at $N=\ensuremath{\infty}$, the renormalized coordination number introduced by Yasuda et al. [Phys. Rev. Lett. 94, 217201 (2005)] is a universal number in the limit of ${J}^{\ensuremath{'}}∕J\ensuremath{\rightarrow}0$. Moreover, similar scaling relations proposed by Hastings and Mudry [Phys. Rev. Lett. 96, 027215 (2006)] are derived at $N=\ensuremath{\infty}$ for the three-dimensional static spin susceptibility at the wave vector $(\ensuremath{\pi},\ensuremath{\pi},0)$, as well as for the instantaneous structure factor at the same wave vector. We then use

1∕N

corrections to study the relation between interplane coupling, correlation length, and critical temperature, and show that the universal scaling relations lead to logarithmic corrections to previous mean-field results.