Scaling relations in quasi-two-dimensional Heisenberg antiferromagnet

TL;DR

This paper uses large-N expansion of the quantum nonlinear sigma model to derive universal scaling relations for quasi-two-dimensional Heisenberg antiferromagnets, revealing logarithmic corrections to mean-field predictions.

Contribution

It establishes universal scaling relations at N=∞ for quasi-2D antiferromagnets and incorporates 1/N corrections to refine understanding of interplane coupling and critical behavior.

Findings

Universal renormalized coordination number at N=∞

Scaling relations for static spin susceptibility and structure factor

Logarithmic corrections to mean-field results from 1/N corrections

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 $J'/J\to 0$. 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.