# What is short-range antiferromagnetic order?

I know what anti-ferromagnetism is. But in a paper I came across "short-range antiferromagnetic order". Can someone please explain to me what it is or suggest me the book/(or any material).

• Can you link to the paper so we can see the context? – taciteloquence Apr 12 at 7:28

As far as I have seen, the term "short-range antiferromagnetic order" is not necessarily very well defined. It would most likely refer to the staggered spin correlations $$C_s = (-1)^r \vec S_i \cdot \vec S_{i+r}$$ decaying with an exponential. $$C_s \propto e^{-r/\xi}$$. It's definitely not long range order (where $$C_s(r\to \infty) \neq 0$$ nor is it quasi-long-range order $$C_s \propto r^{-b}$$.
Magnetic ordering is usually measured using a spin-spin correlation function, like $$S_{i,j} = \langle S_z(r_i) s_z(r_j) \rangle$$. If the system has antiferromagnetic order, the Fourier transform of this correlator will have a peak of $$k = \pi$$ for a a one-dimensional system, or at $$(\pi, \pi )$$ in two dimensions etc. If the system is perfectly ordered, this peak will be a $$\delta$$-function. If the ordering reduces with the separation $$| r_i - r_j |$$, however, the peak will be broadened. If the correlator decays as a power-law of the separation - one of the best-known examples is the Kosterlitz-Thouless transition - the ordering is often called "quasi-long range order". However, if the decay is exponential, there is only antiferromagnetic order over separations comparable to the length-scale of the exponential, and this is called "short-range ordering".