Scaling relations in quasi-two-dimensional Heisenberg antiferromagnet

Abstract

The large-N expansion of the quasi-two-dimensional quantum nonlinear $\sigma$ model (QNLSM) is used in order to establish experimentally applicable universal scaling relations for the quasi-two-dimensional Heisenberg antiferromagnet. We show that, at $N=\infty$, the renormalized coordination number introduced by Yasuda \textit{et al.}, Phys. Rev. Lett. \textbf{94}, 217201 (2005), is a universal number in the limit of $J^{\prime }/J\to 0$. Moreover, similar scaling relations proposed by Hastings and Mudry, Phys. Rev. Lett. \textbf{96}, 027215 (2006), are derived at $N=\infty$ for the three-dimensional static spin susceptibility at the wave vector $(\pi ,\pi ,0)$, 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.

16 pages, 4 figures, reference to cond-mat/0606341 added

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• Temperature dependence of the $(\pi ,0)$ anomaly in the excitation spectrum of the 2D quantum Heisenberg antiferromagnet
• Quantum magnetism on small-world networks